Probability

More than One Event

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

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

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

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?

2025 October(J08) Math Question 12

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

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

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?

35 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. 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. 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. 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

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

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

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

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?

2024 September(H11) Math Question 35

2011 June(69F) Math Question 36

Carina rolls 2 cubes. Each has the whole numbers from 1 through 6 on its faces, 1 per face. The faces of each cube are equally likely to land up. What is the probability that the sum of the numbers on the faces landing up is 3 or more?

35 February(Z14) Math Question 36

All students in a high school responded either "Yes" or "No" to the question "Are you studying enough?" The table below gives the number of students in each grade who responded. Two numbers in the table are represented by x and y. The probability that a randomly selected student from this high school is in 11th grade given that the student responded "No" is 75/267. One of the following is the value of x. Which one?

2024 June(G20) Math Question 36

37. Mr. and Mrs. Smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days ?

2017 April(74F) Math Question 37

A restaurant conducted a survey to determine whether its customers like or dislike corn bread and whether they like or dislike banana bread. The table below shows the results of the survey. Given that a customer selected at random from those surveyed likes corn bread, what is the probability that the customer dislikes banana bread?

2024 September(H11) Math Question 37

39. Suppose a person will be chosen at random from these 560 residents. Which of the following values is closest to the probability that the person chosen will NOT be a high school student and will NOT have replied with no opinion?

2017 June(74C) Math Question 39

One registered person will be randomly selected to win a raffle prize. Which of the following expressions is equal to the probability that the selected person did NOT finish the race?

2023 April(F11) Math Question 43

Maya's digital music library has a total of 249 songs. Her library has 64 songs that are remixes and 85 hip-hop songs. Of the hip-hop songs in her library, 25 are remixes. How many songs in her library are NEITHER remixes NOR hip-hop songs?

2024 June(G20) Math Question 43

Let K and J be independent events. Given that P(K) = 0.40 and P(J) = 0.20, what is the probability that K and J will both occur? (Note: P(A) is the probability that Event A will occur.)

2023 September(G01) Math Question 44

46. Use the following information to answer questions 46–48. Data from a random sample of 335 car owners in a certain city are listed below. The table indicates the number of owners in 3 age brackets (16−25, 26−45, 46−60) who own cars from 3 car companies (A, B, C) in this city. Each owner in the sample owns only 1 car. Data from a random sample of 335 car owners in a certain city are listed below. The table indicates the number of owners in 3 age brackets (16−25, 26−45, 46−60) who own cars from 3 car companies (A, B, C) in this city. Each owner in the sample owns only 1 car. 46. Two car owners from this sample will be chosen at random. Given that no owner is chosen twice, which of the following expressions gives the probability that both owners chosen will be from the same age bracket?

Permutations

2020 December(D03) Math Question 46

47. Yulan will use a bag of 30 solid-colored marbles for a game in which each player randomly draws marbles from the bag. The number of marbles of each color is shown in the table below.

2018 April(A09) Math Question 47

One of the 50 polled shoppers will be selected at random. What is the probability that the selected shopper owned at least 1 dog or cat?

2024 April(Z13) Math Question 47

A square dartboard is red and white, as shown below. Each 4-inch-long side of the red square is parallel to 2 sides of the white square and is 3 inches from the closest side of the white square. A dart will be thrown randomly and will land on the dartboard. What is the probability that the dart will land on the red square?

2024 June(G20) Math Question 47

48. The probabilities that each of 2 independent events
will occur are given in the table below.

2019 June(B02) Math Question 48

49. A professional baseball team will play 1 game Saturday • and 1 game Sunday. A sportswriter estimates the team has a 60% chance of winning on Saturday but only a 35% chance of winning on Sunday. Using the sportswriter’s estimates, what is the probability that the team will lose both games?

2017 June(74C) Math Question 49

Each student in Mrs. O'Malley's first-period Civics class draws 1 tag at random from each of 2 bowls to determine seating location in the class. The tag drawn from the first bowl is the row number of a student's seat; the 28 tags in the first bowl have an equal distribution of the numbers 1, 2, 3, 4, 5, 6, and 7. The tag drawn from the second bowl is the seat number within the row determined by the first tag; the 28 tags in the second bowl have an equal distribution of the numbers 1, 2, 3, and 4. What is the probability that the first student who draws will have a seating location that is in Row 5, but NOT in Seat 1?

2024 April(Z13) Math Question 50

53. A box contains 6 identically sized, solid-colored balls. One ball is green, 2 are yellow, and 3 are red. A ball is drawn at random and returned to the box, then a second ball is drawn at random. What is the probability that the first ball is red and the second ball is green?

2015 December(72E) Math Question 53

2019 April(Z15) Math Question 54

Of the 300 juniors at Northeast High School, 130 are taking both math and English, 139 are taking both science and English, 119 are taking both math and science, and 98 are taking all 3 courses. Only 18 students are taking none of the 3 courses. One of the juniors from Northeast High School will be chosen at random. What is the probability that the chosen student is taking exactly 1 of these 3 courses?

2023 September(G01) Math Question 55

2019 December(C03) Math Question 56

56. At Wafer Technologies, identification codes each consist of the following sequence: 1 digit, 4 letters, 1 digit. For any 1 code, the digits (0-9) may be the same, but the letters, each from the English alphabet, must all be different. Which of the following expressions gives the probability that a randomly selected identification code contains the word MATH, spelled correctly?

2016 December(74H) Math Question 56

58. Five balls, numbered 1, 2, 3, 4, and 5, are placed in a bin. Two balls are drawn at random without replacement. What is the probability that the sum of the numbers on the balls drawn is 7 ?

2018 June(A11) Math Question 58

2018 December(B05) Math Question 58

A shirt will be randomly selected from a display of 23 shirts. The probability that the selected shirt will be long-sleeved is 13/23. The probability that the selected shirt will be white is 8/23. The probability that the selected shirt will be long-sleeved and white is 3/23. What is the probability that the selected shirt will be long-sleeved or white or both?

2024 June(G20) Math Question 58

A store that sells office furniture tracks the number of bookcases sold each day for a year and then prepares the data table below. Which of the following is closest to the number of bookcases the store can expect to sell in 100 randomly selected days?

More than One EventProbabilityACT math questions

2024 September(H11) Math Question 2

2023 April(F11) Math Question 4