Probability

More than One Event

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

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

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

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

2013 December(71E) Math Question 32

2019 April(Z15) Math Question 33

2011 June(69F) 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

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

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

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

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

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 ?

More than One EventProbabilityACT math questions

2013 June(71C) Math Question 18

2016 April(73E) Math Question 19