ACT Math · Statistics & Probability
Probability and counting practice questions
Each free question on this page comes with its answer and a full explanation.
- Question 29A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If one marble is drawn at random, what is the probability…
- Question 31Two fair six-sided dice are rolled. What is the probability that the sum of the two dice is at least 10?
- Question 32In how many ways can a committee of 3 people be chosen from a group of 8 people?
- Question 33A game costs $5 to play. A player wins $20 with probability 0.15, and otherwise wins nothing. What is the expected net gain or…
- Question 71Of 60 students, 35 play a sport, and 20 of those 35 also play an instrument. If a student who plays a sport is selected at…
- Question 73In a race with 5 runners, in how many different ways can 1st, 2nd, and 3rd place be awarded?
- Question 74Events A and B are independent, with P(A) = 0.3 and P(B) = 0.6. What is P(A and B)?
- Question 115The probability of rain tomorrow is 0.35. What is the probability that it does NOT rain?
- Question 116Of 100 people surveyed, 60 like coffee, 45 like tea, and 25 like both. What is the probability that a randomly selected person…
- Question 117A coin is flipped and a six-sided die is rolled. How many total outcomes are possible?
- Question 118A bag contains 3 red marbles worth 2 points each if drawn, and 7 blue marbles worth 0 points. If one marble is drawn at random,…
- Question 157A bag contains 5 red marbles and 5 blue marbles. A marble is drawn, its color noted, and then replaced before a second marble is…
- Question 160A fair coin is flipped 3 times. What is the probability of getting at least one head?
- Question 162A committee of 2 men and 2 women is to be chosen from a group of 5 men and 6 women. How many different committees are possible?
- Question 201A spinner has 8 equal sections numbered 1 through 8. What is the probability that a spin lands on a multiple of 3?
- Question 203Of 50 students, 30 play soccer, 25 play basketball, and 10 play both sports. How many students play neither sport?
- Question 204A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that the…
- Question 207A standard deck of 52 cards is shuffled, and one card is drawn. What is the probability of drawing a face card (jack, queen, or…
- Question 266A square dartboard has side length 10. A circle with radius 3 is inscribed somewhere on the board. If a dart lands at a random…
- Question 271How many different ways can 6 numbers be chosen from a set of 49, without regard to order?
- Question 274Events A and B are mutually exclusive, with P(A) = 0.3 and P(B) = 0.45. What is P(A or B)?
- Question 276A game show wheel has three outcomes: winning $100 with probability 0.1, winning $20 with probability 0.3, and winning $0 with…
- Question 280A student takes two independent tests. The probability of failing test A is 0.2, and the probability of failing test B is 0.3.…
- Question 281Of 200 people surveyed, 120 own a car, 80 own a bicycle, and 30 own both. If a person who owns a bicycle is selected at random,…
- Question 285A weather forecast gives a 30% chance of rain on each of the next two days, with the two days independent of each other. What is…