Probability

2010 June(68C) Math Question 1

1. The numbers 1 through 15 were each written on individual pieces of paper, 1 number per piece. Then the 15 pieces of paper were put in a jar. One piece of paper will be drawn from the jar at random. What is the probability of drawing a piece of paper with a number less than 9 written on it?

2021 April(Z04) Math Question 1

1. The 32-member French Club is meeting to choose a student government representative. The members decide that the representative, who will be chosen at random, CANNOT be any of the 5 officers of the club. What is the probability that Luis, who is a member of the club but NOT an officer, will be chosen?

2016 December(74H) Math Question 1

2010 December(69A) Math Question 1

2. A wallet containing 2 five-dollar bills, 9 ten-dollar bills, and 5 twenty-dollar bills is found and returned to its owner. The wallet's owner will reward the finder with 1 bill drawn randomly from the wallet. What is the probability that the bill drawn will be a twenty-dollar bill?

2017 June(74C) Math Question 2

2. The 35-member History Club is meeting to choose a student government representative. The members decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club. What is the probability that Hiroko, who is a member of the club but NOT an officer, will be chosen?

2017 April(74F) Math Question 2

2012 April(70G) Math Question 2

During a certain game, the probability of randomly drawing Card A is 1/8. What is the probability of randomly drawing a card that is NOT Card A?

2024 September(H11) Math Question 2

3. In his costume supplies, Elmo the clown has 4 noses, 3 pairs of lips, and 2 wigs. A clown costume consists of 1 nose, 1 pair of lips, and 1 wig. How many different clown costumes can Elmo make?

2017 June(74C) Math Question 3

When a fair coin is flipped a large number of times, the number of heads should be approximately equal to the number of tails. Assume that the fairness of a particular coin is being investigated. Which of the following results provides the strongest evidence that the coin is not fair?

2025 October(J08) Math Question 4

A yogurt shop has 6 flavors of yogurt and 5 toppings. Each sundae consists of 1 yogurt flavor and 1 topping. Jaylen decided to surprise Takoda with a sundae, but he did not know her preferences. Given that Takoda has a preference of 1 flavor of yogurt and 1 topping from those available in the shop, what is the probability that Jaylen will choose the topping and yogurt that Takoda prefers?

2023 April(F11) Math Question 4

On a digital music player there are 153 rap songs, 72 country songs, 14 jazz songs, and 121 rock songs. Given that the player is set to randomly shuffle the song selection, what is the probability, rounded to the nearest thousandth, the 1st song played will be a country song?

2024 September(H11) Math Question 4

5. A wallet containing 5 five-dollar bills, 7 ten-dollar bills, and 8 twenty-dollar bills is found and returned to its owner. The wallet's owner will reward the finder with 1 bill drawn randomly from the wallet. What is the probability that the bill drawn will be a twenty-dollar bill? DO YOUR FIGURING HERE.

2017 April(74F) Math Question 5

2009 April(66F) Math Question 5

2020 July(C01) Math Question 5

2019 April(Z15) Math Question 5

5. A certain committee is composed of 9 juniors and 11 seniors. Two different members of the committee will be randomly selected for 2 different leadership roles. Given that the 1st member who will be selected is a senior, what is the probability that the 2nd member who will be selected is a junior?

2020 December(D03) Math Question 5

6. A bag contains exactly 18 solid-colored buttons: 3 red,
5 blue; and 10 white. What is the probability of
randomly selecting 1 button that is NOT white?

2019 June(B02) Math Question 6

2013 December(71E) Math Question 6

2013 April(71G) Math Question 6

All 26 students in a high school music department are enrolled in choir, band, or both. Of the 26 students, 14 are enrolled in choir and 18 are enrolled in band. How many are enrolled in both choir and band?

2024 December(H31) Math Question 6

7. A bag contains 10 pieces of flavored candy: 4 lemon, 3 strawberry, 2 grape, and 1 cherry. One piece of candy will be randomly picked from the bag. What is the probability the candy picked is NOT grape flavored?

2015 June(73C) Math Question 7

2019 December(C03) Math Question 7

2012 June(70C) Math Question 7

2010 April(68G) Math Question 7

Jesse has 4 shirts, 8 pairs of jeans, and 4 coats, which all go together well. How many different outfits consisting of 1 of his 4 shirts, 1 of his 8 pairs of jeans, and 1 of his 4 coats are available for Jesse to wear?

2024 December(H31) Math Question 7

8. Yvette has 6 pairs of leggings, 2 pairs of shoes, and 6 T-shirts, which all go together well. How many different groupings consisting of 1  of her 6 pairs of leggings, 1  of her 2 pairs of shoes, and 1  of her 6 T-shirts are available for Yvette to wear?

Combinations

2021 April(D05) Math Question 8

8. What is the value of the expression __8_!_ ? (4!)2

2021 June(D06) Math Question 8

The probability that event A will occur is 0.20. If event A occurs, the probability that event B will occur is 0.30. What is the probability that event A will occur and event B will occur?

2026 April(R4A) Math Question 8

2011 April(67F) Math Question 9

2018 December(B05) Math Question 9

2009 December(68A) Math Question 10

10. Tammy will draft 1 player at random from a list of 20 players for her fantasy football team. Each player in the list plays only l position. The number of players who play a particular position is given in the table below. What is the probability that the player Tammy drafts will be a kicker or a receiver?

2016 December(74H) Math Question 10

The probability that a certain basketball player will make any given free throw is 0.8. Based on this probability, how many free throws should this player expect to have to attempt in order to make 20 free throws?

2026 February(Z14) Math Question 10

2019 December(C03) Math Question 11

11. A bag contains 8 red marbles, 9 yellow marbles, and 7  green marbles. How many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is 3/5 ?

2021 April(Z04) Math Question 11

A certain committee is composed of 11 juniors and 79 seniors. Two different members of the committee will be randomly selected, each for a different leadership role. Given that the 1st member selected is a junior, what is the probability that the 2nd member selected will be a senior?

2026 April(R4A) Math Question 11

2009 June(67C) Math Question 12

2025 October(J08) Math Question 12

13. A box contains 3 red, 2 white, and 5 blue beads, each of which is a solid color. Miguel will randomly remove 1 bead from the box, record the color of the bead, and return the bead to the box. Miguel will complete this process 50 times. How many times should Miguel expect to record a bead color that is NOT white?

2014 December(72G) Math Question 13

2010 June(68C) Math Question 14

14. A bowl contains 6 red beads, 8 black beads, and a number of green beads. There are no other beads in the bowl. The probability of randomly choosing a black bead from the bowl is 1/3. How many green beads are in the bowl?

2015 April(73G) Math Question 14

15. Miriam conducted a survey of the students in her 8th-grade class to determine which of 7 Olympic sports were the most popular. Each student who responded to the survey selected 1 Olympic sport as his or her favorite. The circle graph below shows the number of students who selected each of the 7 Olympic sports. A total of 40 students responded to the survey. To the nearest 0.1%, what percent of the students who responded to the survey selected Basketball?

2013 June(71C) Math Question 15

2019 April(Z15) Math Question 17

18. Lena will pick 1 card at random from a pack of 25 baseball cards. Each card features the fielding position for 1 of 25 different baseball players. Each player in the pack has only 1 fielding position. The table below lists the frequency of fielding positions in the pack. What is the probability that the card Lena picks will feature an outfielder or a pitcher?

2018 June(A11) Math Question 18

18. How many different possible orders of pasta can a person get?

2015 December(72E) Math Question 18

18. A spinner dial from a game is shown in the figure below. Each numbered sector of the circle has the same central angle measure. If the arrow on the spinner dial is spun randomly, what is the probability the arrow will point to a sector whose number is both a multiple of 3 and a multiple of 4 ?
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2013 June(71C) Math Question 18

A certain company manufactured 1,000 vacuums and recorded the number of those vacuums sold within 5 months. The company's findings are summarized in the table below. What is the probability 1 of the 1,000 vacuums was sold 3 or 4 months after it was manufactured?

2024 December(H31) Math Question 18

19. A batch of 100 defective computer chips consisting of 2 types (I and II) and made by 2 companies (A and B) was selected, and it was determined how many of each type of chip was made by each company. The results are displayed in the table below.

2016 April(73E) Math Question 19

19. By May 15, Ms. Chen had enrolled her 2 children for camp. One child was in Grade 3, and the other was in Grade 4. For each grade, the names of all the children enrolled by May 15 will be entered into a drawing for a free T-shirt. For each grade, 1 name will be randomly drawn. What is the probability that the names of both of Ms. Chen’s children will be drawn?

Independent Events

2021 December(E23) Math Question 19

2019 April(Z15) Math Question 20

21. A bag contains 10 solid-colored marbles of the same
size: 3 red, 2 green,.1 yellow, and 4 blue. Which of the
following expressions gives the probability of drawing,
at random and without replacement, a blue marble on
the 1st draw, a green marble on the 2nd draw, and a
blue marble on the 3rd draw?

2019 June(B02) Math Question 21

2012 December(71A) Math Question 21

21. A set of numbers consists of all the odd integers that are greater than 1 and less than 21. What is the probability that a number picked at random from the set will be divisible by 3 ?

2015 April(73G) Math Question 21

22. A physical education teacher recorded the distances, in
inches, that her students jumped during a long jump
lesson. The distances of 1 jump by each of the students
are represented in the stem-and-leaf plot below.

2019 June(B02) Math Question 22

22. The mayor of Westbrook is deciding how to assign the 6 council members to the row of seats below.

2018 June(A11) Math Question 22

22. Sets A, B, and C are defined below. A = {1, 2, 3, 4, 5, 6, 7, 8, 9} B = {2, 4, 6, 8} C = {4, 8} A number will be randomly selected from A. What is the probability that the selected number will be an element of C and an element of B ?

Sets

2020 December(D03) Math Question 22

23. Sets A, B, and C are defined below. A = {1, 2, 3, 4, 5, 6} B = {2, 4, 6} C = {1, 2}  A number will be randomly selected from set A. What is the probability that the selected number will be an element of set B and an element of set C ?

2021 April(D05) Math Question 23

A cleaning company sends out advertisements to potential customers. The table lists the probability of an advertisement leading to a certain amount of revenue. To the nearest cent, what is the expected value of the revenue generated from an advertisement sent to a potential customer?

2025 October(J08) Math Question 23

A basket contains 3 red apples, 4 green apples, and 2 yellow apples. An apple is drawn at random, eaten, and then another apple is randomly drawn. If the first apple is red, what is the probability the second apple is yellow?

2026 February(Z14) Math Question 23

What is the probability that the snowman will melt today?

2024 April(Z13) Math Question 23

A theme park is building 3 new rides: the Thunder, the Gateway, and the Cyclops. Guests to the park were asked to respond "yes," "no," or "maybe" when asked if they would like to experience one of these rides. The results are shown in the table below. To the nearest 0.01, what is the probability that a randomly selected guest who was asked about the Gateway responded "yes"?

2024 December(H31) Math Question 23

24. The figure below shows 3 different views of the same fair cube. Each face of the cube has 1 design drawn on it. The cube will be rolled once. What is the probability that a face showing a star (*) will be on top?

2014 April(71H) Math Question 24

2019 April(B04) Math Question 24

24. One day will be randomly selected from the 7 days in a week. Then 1 month will be randomly selected from the 12 months in a year. What is the probability that the selected day will be Tuesday and the selected month will be January?

2021 June(D06) Math Question 24

25. At East High School, the 20 cast members of the spring musical sold 2 types of tickets—student and adult—for the Friday night and Saturday night performances. The price of each student ticket was $2 and the price of each adult ticket was $3. The table below gives the number of tickets sold, by type and by night. The stem-and-leaf plot below shows the number of tickets, regardless of type, sold by each of the 20 cast members. The auditorium where the spring musical will be performed has 10 seats in the 1st (front) row. Each row behind the 1st row has 4 more seats than does the row in front of it. Suppose 1 cast member will be picked at random from the 20 cast members who sold tickets to receive a prize. What is the probability of picking a cast member who sold more than 30 tickets?

2014 December(72G) Math Question 25

2010 April(68G) Math Question 25

25. Audrey will take biology, algebra, and Spanish next year. Audrey will have 1 of the 3 teachers who teach biology, 1 of the 4 teachers who teach algebra, and I of the 2 teachers who teach Spanish. From among these 9 teachers, how many possibilities are there for Audrey's 3 teachers for the 3 classes?

2015 April(73G) Math Question 25

2018 December(B05) Math Question 25

25. Of the 900 students enrolled at Sierra Elementary School, 45% live south of Highway R. Of the students who live south of Highway R, 20% do NOT ride the bus to school. How many students who live south of Highway R ride the bus to school?
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2016 April(73E) Math Question 25

On the local car dealer's lot, there are only 25 cars with power windows and only 17 cars with heated seats. The number of cars on the lot with both power windows and heated seats must be:

2023 April(F11) Math Question 25

26. A bag contains 16 red’marbles, 7 yellow marbles, and 19 green marbles. How many additional red marbles must be added to the 42 marbles already in the bag so that the probability of randomly drawing a red marble

2017 June(74C) Math Question 26

26. An 8-sided game piece with faces numbered from 1 to 8 is rolled twice. What is the probability that an 8 is rolled both times? (Note: Assume that each side has an equally likely chance of being rolled.)

2021 April(D05) Math Question 26

26. About 1.48 × 108 square kilometers of Earth’s surface is land; the rest, about 3.63 × 108 square kilometers, is water. If a returning space capsule lands at a random point on Earth’s surface, which of the following is the best estimate of the probability that the space capsule will land in water?

2021 April(Z04) Math Question 26

2011 June(69F) Math Question 27

2019 April(B04) Math Question 27

2013 April(71G) Math Question 28

A jar of solid-colored marbles contains some yellow marbles, 21 blue marbles, 40 red marbles, and 14 green marbles. The probability of randomly drawing a green marble is 2/15. How many yellow marbles are in the jar?

2023 April(F11) Math Question 28

2019 June(72F) Math Question 29

2013 April(71G) Math Question 29

30. A committee will be selected from a group of 12 women and 18 men. The committee will consist of 5 women and 5 men. Which of the following expressions gives the number of different committees that could be selected from these 30 people?

2016 December(74H) Math Question 30

2013 April(71G) Math Question 30

Shown below are 2 fair dice. One has 6 faces, each numbered with a different integer from 1 through 6. The other has 8 faces, each numbered with a different integer from 1 through 8. What is the probability that, when the 2 dice are rolled, the sum of the faceup integers will be 12?

2024 December(H31) Math Question 30

2010 June(68C) Math Question 31

A spinner has 10 congruent sectors that have alternating shading and are numbered 1 through 10, as shown below. The pointer is spun. Given that the pointer stops in a shaded sector, what is the probability that the pointer stops in a sector that is a multiple of 3?

2024 December(H31) Math Question 31

2013 December(71E) Math Question 32

2009 June(67C) Math Question 32

2020 July(C01) Math Question 32

A 2-digit number will be formed by randomly selecting each digit from the set {2, 3, 9}. What is the probability that the number formed will be 99?

2024 April(Z13) Math Question 32

2019 April(Z15) Math Question 33

33. A package of candy contains pieces each of which is 1 of 6 possible colors: brown, red, green, yellow, orange, and blue. In each package, 1/3 of the pieces are brown and the remaining pieces have an even
distribution of the other 5colors. What is the probability that a piece drawn randomly from the package is red?

2021 June(D06) Math Question 33

2009 April(66F) Math Question 33

Event W consists of 14 simple events. Event X consists of 11 simple events, none of which are in event W. Event Y is the intersection of events W and X, and event Z is the union of events W and X. Which of the following statements is true? (Note: Given that event E consists of n simple events, |E| = n.)

2025 October(J08) Math Question 33

34. Which of the following values is closest to the number of seconds it will take for the airplane to fly from C to the point directly above the radar station at A ?

2017 December(A10) Math Question 34

34. A bag contains several marbles. On 3 successive draws with replacement, a red marble is drawn from the bag each time. Which of the following statements must be: true about the marbles in the bag?

2018 April(A09) Math Question 34

34. To make a 750-piece jigsaw puzzle more challenging, a puzzle company includes 5 extra pieces in the box along with the 750 pieces, and those 5 extra pieces do not fit anywhere in the puzzle. If you buy such a puzzle box, break the seal on the box, and immediately select 1 piece at random, what is the probability that it will be 1 of the extra pieces?

2014 June(72C) Math Question 34

2020 June(C02) Math Question 34

A group of 4 friends decide to go to a movie. After buying their tickets, they find 5 empty chairs in the theater. How many different seating arrangements are possible if the 4 friends sit, at most 1 person per chair, in these 5 chairs?

2026 February(Z14) Math Question 35

At an ice-cream shop, patrons can purchase a single scoop of 1 ice-cream flavor and 1 topping for $2.99. The owner recorded the number of different ice-cream flavors and 1-topping combinations that were purchased, as shown in the table below. To the nearest 0.01, what is the probability that a randomly selected patron purchased a scoop of vanilla ice cream topped with sprinkles?

ProbabilityThere are 162 ACT math questions under Probability

Sub-topics

2010 June(68C) Math Question 1

2021 April(Z04) Math Question 1