Probability Concepts folder

At a deli, you have a choice of turkey, roast beef, or ham on your sandwich and a choice of potato chips or corn chips on the side. How many different ways can you order a sandwich and chips??

How many outcomes are possible? (coin, spinner)

a dime and a quarter are tossed

If a 6-sided number cube is also rolled, how many outcomes are possible?

As part of Ella's birthday present, her mother tells her she can choose two days, Monday through Friday, that she doesn't have to do her chores. How many combinations of days can she choose?

Each spinner is spun once. Find the probability of spinning blue both times.

Find P(tails, vowel).

A standard six-sided number cube is rolled and a coin is tossed. What is the probability that the cube shows a 3 and the coin is tails?

Find P(heads, A).

How many combinations of two books can be chosen from a group of four on a shelf?

John, Keri, and Carlos are working on a project for school. How many ways can they decide which two of them will give the oral report to the class?

How many outcomes are possible? (coin, tile)

small, medium, large, and extra large in blue, red, or green

At Healthy Option Family Restaurant, kids can get a number of kiddy meal choices. Refer to the tree diagram. How many different kinds of kiddy meals are there?

What is the probability that the first spinner will land on an odd number and the second spinner will land on a vowel??

P(3 and tails) ▢ P(5 and heads)

How many possible outcomes are there for each toss?

P(4, then 4)

P(number greater than 5 and heads) ▢ P(prime number and tails)

What is the probability of the coin landing tails up both times?

P(odd, then odd)

P(both scissors)

P(Player 1 rock, Player 2 paper)

P(even number, red)

What is the probability that the first spinner will land on A, the second spinner will land on an even number, and the third spinner will land on Blue?

P(2, red)

What is the probability that the first spinner will land on B, the second spinner will land on 3, and the third spinner will land on Green?

You roll a number cube twice.?

A store has 11 kinds of bagels and 5 kinds of spreads. How many different combinations of a bagel and 1 spread can be made?

There are 4 choices for skis, 2 choices for bindings, and 5 choices for boots. How many ways can skis, bindings, and boots be chosen?

You toss a coin four times.

There are 10 yogurt flavors, 4 syrups, and 5 toppings. How many ways can one flavor, one syrup, and one topping be chosen?

A yogurt shop offers 6 different flavors of frozen yogurt and 9 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?

You toss a coin two times. Find the probability of getting heads on both tosses.

Tamara likes to mix and match her 4 scarves, 3 pairs of gloves, and 2 hats. The colors are in the table On Monday, she randomly picks out a scarf, hat, and a pair of gloves. What is the probability of Tamara choosing a pair of black gloves and a red hat?

Suppose you have more than one kind of shirt and more than one pair of jeans. Which of the following could NOT be the total number of outfits you can make?

To play a game, you spin a spinner and take a card. The spinner has equal sections that tell you to move 1, 2, 3 or 4 spaces. The cards read Free Turn, Lose a Turn, or No Change. Find the probability that you move 3 spaces and lose a turn.

choosing a letter from the word SPACE and choosing a consonant from the word MATH?

What is the probability of having 2 boys and 1 girl?

Hunter is a big fan of the Houston Astros baseball team and wears a different jersey and cap every time he goes to a game. The table shows the number of jerseys and caps that Hunter owns. How many jersey/cap combinations can Hunter wear?

picking a number from 1 to 4 and choosing the color red, green, or yellow

rolling a number cube and choosing one of two cards marked X and Y

tossing a coin and rolling a number cube

choosing black, blue or brown socks with boots, gym shoes or dress shoes

tossing a quarter, a nickel and a dime

Craig stops at a gas station to fill his tank. He must choose between full-service and self-service and between regular, midgrade and premium gasoline. How many possible combinations are there?

choosing a purple, green, black or silver mountain bike having 10, 18, 21 or 24 speeds

John is getting his ATM card activated. He must select a password containing 4 nonzero digits to be able to use the card. How many passwords are allowed if no digit may be used more than once??

Tom goes to a stationery shop to purchase a set of watercolors and a paintbrush. There are 3 different brands of watercolors each available in 2 different size packs. There are 2 brands of paintbrushes each available in 8 different sizes. How many ways Tom can choose a pack of watercolors and a paintbrush?

A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many different combinations are possible?

There are 9 children playing in a playground. In a game, they all have to stand in a line such that the youngest child is at the beginning of the line. How many ways can the children be arranged in the line?

In a refrigerator, there are 6 bottles of soft drinks (each a different brand) and 8 cans of juice (each a different type). How many combinations can be made with one soft drink and one fruit drink?

A garment company has been contracted to make uniforms for players of a football tournament. There are 12 different colors and 12 designs selected for the uniforms. How many combinations of colors and designs can be made for the uniforms of different teams?

In how many orders can 7 chapters be arranged in the index of a textbook if the chapter on probability is to be listed in the middle of the series of chapters?

For a college debate competition, Daniel must select one topic of six topics to speak at the first level. He must also select a different topic from the same list to speak at the second level of the competition. How many ways can he choose the topics for the two levels?

Alan's online test has 10 true-false questions and 5 multiple-choice questions. Each multiple-choice question has 4 different answer choices. How many different choices for answering the 15 questions are possible?

choosing the color and size of a pair of shoes

In how many ways can 6 members of a dance group in different color costumes be made to stand in a line if the first person is in a yellow costume?

choosing the winner and runner-up at a dog show

In how many ways can 5 toy animals be arranged in a line on a shelf if one of the toys is a tortoise and it must be at the end of the line?

Joe wants to buy a pair of shoes. His shoe size is available in 4 designs and 5 colors in a particular shop. From how many combinations of designs and colors can he choose?

In a high school, a student has an option of 3 foreign languages, training for 4 different musical instruments, and 6 types of outdoor activities. How many ways can a student select a foreign language, an instrumental training, and an outdoor activity?

Phone numbers consist of a three-digit area code followed by seven digits. If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? How did you come up with your answer??

When dealing with the occurrence of more than one event, what is one way to determine all possible combinations?

What is the sample space of the experiment? What is the probability of getting a 1 or a 2?

A card is picked at random from a standard deck of 52 cards. What is the probability of picking a face card (King, Queen, or Jack)?

Does this table represent a probability distribution? Explain your answer.

You roll a die and toss a penny.

In a single experiment, a die is tossed and a spinner with the letters A, B, and C is spun. Each letter is equally likely. Find the sample space and then find the probability of getting a B.

You spin a spinner with four equal sections labeled 1, 2, 3, and 4 and toss a dime.

When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let x be the product of the numbers. Let P be the probability of the desired outcome. Compare the following charts and determine which chart shows the probability distribution for the product of the two numbers.

If you flip a coin ten times, how many different sequences of heads and tails are possible?

A bag contains five green marbles and four red marbles. The marbles are randomly selected one at a time. What are the odds in favor of picking the green marble on the first selection??

Suppose you roll a standard number cube. What are the odds that the number is a multiple of 3?

The probability of choosing a red marble from a bag of marbles is 2/5. What are the odds of choosing a red marble from the bag?

Each card in a set of 7 cards has one letter from the word Florida. What are the odds of choosing a card that does not have a vowel?

The Lindbergh High School carnival has a raffle for one trip to a theme park. The number of students buying raffle tickets in each class is given in the table below. Each student has a single ticket. What are the odds the raffle winner will be from the freshmen class?

A student is chosen at random from a class of 10 boys and 20 girls. What are the odds that a girl is not chosen?

The letters in Montgomery, Alabama are written on slips of paper, one letter per slip. What are the odds of drawing an A?

A student is chosen at random from a class of 10 boys and 20 girls. What are the odds that a boy is chosen?

Find the odds of a coin landing heads up when you toss a coin?

The weatherman says there is a 30% chance of rain tomorrow. Find the odds that it will rain tomorrow.

Suppose you choose a letter at random from the word Indiana. What are the odds that the letter you choose will be an a?

You buy a raffle ticket to win a computer. One of 200 tickets will be drawn from a box to determine the winner. What are the odds that you win?

Probability can?

Odds and probability are the same thing.

What is the probability that Holly will not be chosen?

What are the odds in favor of James being chosen?

Odds can be written as a fraction, percent, or decimal.

What are the odd's against Holly being chosen?

Odds compare two quantities.

To find the probability of something happening or not happening you must know

Probability is just another word for "odds".

What are the odds against Oscar winning?

What is the probability that Holly will be chosen?

What is the probability that Oscar will not win?

Odds can

If n is a positive integer, how does nPn comoare to nP(n-1)??

A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?

Which calculation would you use to find ₈P₅?

Which of the following is an outcome for flipping a coin and then rolling a 6-sided number cube?

A ZIP code contains 5 digits. How many different ZIP codes can be made with the digits 0 through 9 if no digit is used more than once?

A sandwich shop has 8 meats and 6 kinds of bread. How many different sandwiches can be made using one type of meat and one type of bread?

In how many ways can the letters M, N, O, P, and Q be ordered?

Area codes for phone numbers are 3 digits long. How many different area codes can be made from the digits 0 through 9 if no digit is used more than once in any single area code?

How many different license plates are possible if a license plate consists of 2 capital letters followed by 5 digits?

Which situation will have the greatest number of possible outcomes?

A circular, rotating serving tray has 5 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the tray??

How many different arrangements can be made using all of the letters in the word IOWA?

Find: 5P4

How many different arrangements can be made using all of the letters in the word TOPIC?

How many different ways can 4 people be seated around a circular table?

Find: 7P5

Find: 6P4

(7 - 5)!

5! x 0!/(4 - 1)!

A circular, rotating serving tray has 8 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the tray?

Evaluate ₁₄C₅.?

Which situation gives you the most possible outcomes?

What does the notation ₇C₃ represent?

What is the value of ₇C₅? [____]

Which expression is used to evaluate 9C6?

9!/7!•2!

What is the relationship between ₁₀C₇ and ₁₀C₃?

You win a prize at a carnival. You can pick 5 prizes off the first shelf, 3 prizes off the second shelf, or 1 prize off the third shelf. You decide to take the first shelf option. If there are 10 different prizes on the first shelf, how many ways can you select your prizes?

6!•8!/7!•4!

What is ₁₂C₅?

From a group of 10 people, 5 are selected at random to participate in a game show. In how many ways can the 5 people be selected??

From a group of 5 freshmen, 3 sophomores, 4 juniors, and 3 seniors, how many 5-person committees are possible?

How many different batting orders are possible if 9 people are chosen from a group of 12 on a baseball team?

Javier's movie collection consists of 3 action movies, 5 comedies, and 9 dramas. In a rush, he randomly grabs 3 movies to bring on a plane flight. What is the probability that he chose 2 action movies and 1 comedy?

An investor would like to invest $60,000 in 2 stocks from a list of 6 suggested by a broker. How many investments of $30,000 each are possible?

A personal identification code consists of five digits (0 through 9). How many codes are possible?

8 people meet, and each person shakes every other person's hand once. How many handshakes occurred?

8 men and 6 women arrive separately in a random fashion to a meeting. What is the probability that the first 4 people to show up are men?

In how many ways can 6 people be arranged in a line?

Given the following circumstances, what counting formula should be used? 1) The order of selection is important. 2) Repetition is not allowed. 3) There are no identical objects.

(a!)^b = a ^b!?

Evaluate: ₈C₄

How many distinct committees of 13 people can be formed if the people are drawn from a pool of 20 people? Use factorials to express the answer.

How many distinct committees of 6 people can be formed if the people are drawn from a pool of 17 people? Use factorials to express the answer.

Evaluate: ₆C₃

Evaluate: 4!/3!1! x 9!/5!4!

Seven cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of seven cards are possible?

Evaluate: ₁₀C₂

8 people from a group of 12 [___________]

a! + b! = b! + a!

₉P₆?

₃₂₅C₁

If a coin is flipped 75 times, in how many ways could there be exactly two tails?

₈C₈

Decide if the following problem is an example of a permutation or a combination. State your rationale. For a study, 4 people are chosen at random from a group of 10 people. How many ways can this be done?

₁₂C₈

What does the symbol for factorial function (n!) mean?

If 6 newborn babies are randomly selected, how many different gender sequences are possible?

How many different four-digit numbers can be made using the digits 1, 2, 3, 4, 5, 6 if no digit can be used more than once?

A shirt company has 3 designs each of which can be made with short or long sleeves. There are 7 color patterns available. How many

₃P₂?

How many different groups of 3 movies can a person rent if there are 12 movies to choose from?

₅P₂

Given ₄C₂, I first apply the formula for combinations, which gives ₄C₂ = 4!/2! (4 - 2)!. This expression simplifies to ₄C₂ = 4!/(2 • 4 - 2 • 2)! = 4!/(8 - 4)! = 4!/4!. Evaluating this, I get a final answer of 1.

A game is played where 26 tiles are in a bag. Each tile has a different letter of the alphabet on it. If you draw 5 letters, what is the probability of the letters being M-U-S-I-C in order, if there is no replacement?

₆C₄

Identify the expression below that represents mPn.

Determine the number of ways to choose a set of 9 pencils from a selection of 10.

A movie rental store has a movie selection that consists of 4 action movies, 3 horror movies, 2 drama movies, and 3 comdies. If you select two movies at random, what is the probability that you select 2 action movies?

Which of the following statements is true for permutations?

According to the 2000 U.S. Census Bureau, 49.65% of Texas residents were male. If one Texan was selected at random in 2000, what is the probability she was female??

Suppose that the probability a seed will germinate is 85%. What is the probability that 7 of these seeds will germinate when 10 are planted?

Which of the following is not a binomial experiment?

What is the theoretical probability of the event that a family with two children has one boy and one girl? Make a tree diagram to help solve the problem.

According to the 2000 U.S. Census Bureau, 49.65% of Texas residents were male. If one Texan was selected at random in 2000, what is the probability he was male?

In a randomly generated sequence of 24 binary digits (0s and 1s), what is the probability that exactly half of the digits are 0?

A die is rolled 30 times. What is the probability of getting x even numbers?

Two events are independent when the following is true:

Suppose that the probability a seed will germinate is 80%. What is the probability that 7 of these seeds will germinate when 10 are planted?

A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips. One paperclip is taken from the drawer and then replaced. Another paperclip is taken from the drawer. Explain why this is an independent or a dependent event.

At a soccer game, a coin is tossed that comes up heads. At the next game, the same coin is tossed and it comes up heads again.? [_____________________]

A new gourmet restaurant offers a choice of 4 main courses and 3 desserts. If you randomly choose a main course and a dessert, what is the probability of choosing the chef's favorite main course and dessert?

A letter is chosen from the words BABY BOY and then replaced. Find P(B and B).

A letter is chosen from the words BABY GIRL and then replaced. Find P(Y and R).

You get three 4's on three rolls of a number cube. [_____________________]

red, then blue

both red

Please select the best answer from the choices provided

The names of all the people at a party one night are put into a hat for a raffle. The first name picked wins the grand prize and is not eligible for any other prizes. The second name picked wins the runner-up prize. [_____________________]

A drawer contains 3 red socks, 4 white socks, and 2 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is blue and the second sock is red?

There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probability that she first pulls a blue marble and then a red marble??

Jamie has three raffle tickets. One hundred tickets were sold. Her name was not drawn for the first prize. What is the probability that her name will be drawn for the second prize?

Bob has a set of 10 colored markers in a backpack. One is yellow and one is blue. What is the probability Bob will reach into the backpack without looking and grab the yellow marker and then reach in a second time and grab the blue marker?

A bag contains 4 marbles. You draw a red marble, put it back in the bag, and then draw a blue marble.

The graph shows the dogs bathed at a dog-grooming business one day. What is the probability that the first two dogs bathed were large dogs?

A school cafeteria has 3 containers of white milk, 5 containers of chocolate milk and 2 containers of apple juice left. Iliana is first in line and Vishal is second. If the drinks are given out randomly, what is the probability that Iliana will get chocolate milk and Vishal will get apple juice?

There is only one copy of each of the 25 magazines in the school library. Peter and Tanya go to the library and each choose one magazine. Peter gets to the library first and chooses Newsweek. When Tanya arrives, she chooses Time.

On a multiple choice test, each question has five possible answers. A student does not know the answers to two questions, so he guesses. What is the probability that the student will get them both wrong?

events for which the outcome of one event does not affect the probability of the other [__________________________]

Franco has 7 quarters in his pocket. Of these, 3 depict the state of Delaware, 2 depict Georgia, 1 depicts Connecticut and 1 depicts Pennsylvania. Franco removes 1 quarter from his pocket and then removes a second quarter without replacing the first. What is the probability that both will be Delaware quarters?

Jane buys a box of 50 donut holes. There are 8 coconut, 7 jelly, 10 honey-dipped, 10 chocolate, 9 powdered sugar, and 6 cinnamon donut holes in the box. Jane's favorite kind is chocolate and her second favorite kind is jelly. What is the probability that she will pick her two favorite kinds of donut holes in the order she likes them? After Jane chooses one, she does not put it back into the box.?

Each player on the soccer team can choose a jersey from the team jersey set, and each jersey contains a different two-digit number from 10 to 99. Chris chooses 32, and then Pat chooses 77.

spinning a 7 on a spinner three times in a row

Victor and Akira are part of a group going to a wrestling match. The group has 3 ringside seats, 3 bleacher seats, and 4 seats in the mezzanine. If the group randomly chooses their seats, what is the probability that both Victor and Akira will sit ringside at the wrestling match?

A bag contains 5 chocolate, 3 peanut butter, 4 oatmeal and 4 sugar cookies. If 2 cookies are selected randomly, what is the probability that they will be the same kind?

Three computers are randomly selected and tested. What is the probability that none are defective if the first and second ones are not replaced after being tested?

The students in gym class each pick lockers for their own use. Juanita picks her locker, and then Serina chooses a locker.

events for which the outcome of the first event affects the probability of the second event [_________________________]

An experiment consists of tossing 2 fair coins, a dime and a quarter. Find the probability that both coins will land the same way.

Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested?

A jar contains 3 chocolate cookies, 5 peanut butter cookies, and 6 coconut cookies. If 3 cookies are selected in succession, what is the probability of selecting chocolate, then peanut butter, and then coconut cookies, if replacement occurs each time??

What is the probability of getting a 4 each time if a die is rolled 3 times?

There are 3 literature books, 4 geography books, and 3 science books on a shelf. If 3 books are chosen at random one after the other, what is the probability that a literature book, a geography book, and a science book are selected if replacement does not take place?

What is the probability of getting a 6 each time if a die is rolled 4 times?

What is the probability of getting tails each time if a coin is tossed 4 times?

A bag contains 4 black, 5 red, and 6 pink balls. If 3 balls are selected one after the other without replacement, what is the probability that 3 red balls are chosen?

A box contains 6 nuts, 8 bolts, and 4 screws. If 3 objects are selected in succession randomly, what is the probability of selecting a nut, then a bolt, then a screw, if replacement occurs each time?

In a game show, cards are displayed showing different prizes. There are 10 cards showing a car, 10 cards showing a holiday trip, and 20 cards showing a house. If the host selects 6 cards in succession without replacement, what is the probability of getting 3 cards showing a car, followed by 2 cards showing a holiday trip, and finally, 1 card showing a house?

A bowl contains 3 red, 8 blue, and 7 black beads. Margaret randomly selects 3 beads one after the other without replacement. Find the probability of getting a red, blue, and black bead, in that order.

Ashley takes her 3-year-old brother Alex into an antique shop. There are 5 statues, 4 picture frames, and 3 vases on a shelf. Alex accidentally knocks 2 items off the shelf and breaks them. Choose the probability best described by: 1/22 [__________________________________________________]

Two standard number cubes are tossed. What is the probability of getting a 5 on the first number cube and an even number on the other??

A toy factory makes a red toy, a green toy, and a blue toy. In a lot of 2,500 toys, 500 were red, 1,500 were green, and 500 were blue. The toy factory has a defect rate of 4%, regardless of the color. If a toy is chosen at random, what is the probability it is blue or red, and defective?

A company makes two versions of a particular software product, a standard version and a deluxe version. Out of 25,000 units shipped, 5,000 were the deluxe version. As a part of a promotion, 1 product in every 500 contained a gift certificate. If a product is chosen at random, which is the probability it will be a standard version with a gift certificate?

In a certain game, a player throws a standard 6-sided number cube twice per turn. What is the probability that the result of the first throw will be a 1, and the result of the second throw will be greater than 3?

Pulling a sock from a drawer, replacing the sock, and pulling another sock from a drawer at random is an example of __________.

For an in-class demonstration, a teacher draws a card from a freshly-shuffled deck. That card is a jack. The jack is not put back in the deck. A student states that the chance of drawing a king is now better than before. What, if anything, is incorrect about the student's logic?

As a part of a contest, a store is giving a special prize if a contestant can roll 3 standard six-sided number cubes, and get the same number on each. What is the probability a contestant will be successful?

Which events are mutually exclusive?

What is the probability of choosing a red marble or a green marble out of a bag containing 5 blue marbles, 3 red marbles, and 1 green marble?

If a person draws 2 cards at random from a standard deck of 52 cards, what is the probability that they get 2 aces?

Consider a fair 6 sided number cube, where each side has one number 1 - 6. All of the even faces are green and all of the odd faces are red. The probability of rolling the number cube and getting a 5 and a green face at the same time is an example of __________.

Which of the following formulas applies to independent events?

What is the probability of rolling a 6 and then a 1 on consecutive rolls of a standard, 6-sided number cube?

A bag contains 30 red tiles, 15 green tiles, and 5 yellow tiles. One tile is drawn and then replaced. Then a second tile is drawn. What is the probability that the first tile is yellow and the second tile is green?

In a certain game, a player throws a standard 6-sided number cube twice per turn. What is the probability that the result of the first throw will be a 5 or a 6, and the result of the second throw will be an even number?

What is the probability of rolling a 3 or an even number when a standard six-sided number cube is tossed? [______]

At a party, there are 2 six-packs of regular cola, 1 six-pack of diet cola, 1 six-pack of cherry cola, and 1 six-pack of vanilla cola. If a can of cola is chosen at random, what is the probability it will be a cherry cola or a vanilla cola?

a multiple of 2 or a multiple of 5?

a multiple of 3 or a multiple of 4

P(a red card or a queen)

P(a 4 or a club)

P(ace or club)

Which of the following best describes: P(exactly one is a 30)

P(a 7 or a heart)

What is the probability of selecting a vowel or a letter from the word random? Hint: Determine if events happen at the same time.

A bag contains 12 pencils, 6 ball pens, and 2 sketch pens. Ronald takes out one writing object from this bag to note down some important information. What is the probability that a ball pen or a pencil is selected?

Which of the following best describes: P(each is a 25)

A card is drawn from a standard deck of cards. P(queen or jack)

A card is drawn from a standard deck of cards. P(6 or ace)

What is the probability of drawing a p or a vowel in the word palindrome? Hint: Determine if events happen at the same time.

Each of the numbers from 1 to 50 is written on a tile and the tiles are placed upside down on the top of a table. If a tile is picked up at random, what is the probability that the number on the tile is a multiple of 7 or a multiple of 8?

A coin is tossed. P(head or tail)