Study ACT on the FlyACT

Study on the flyACTMathematicsProbability and sample spaces

Probability and sample spaces — ACT practice questions

Practice 57 Probability and sample spaces questions in the app

What this topic is

Probability and sample spaces on the ACT Mathematics test covers finding the chance of an event by comparing favorable outcomes with a clearly defined sample space.

A student has to count equally likely outcomes, use combinations when a committee is chosen at random, treat geometric probability as a ratio of areas when a point is selected from a region, and find leftover cases such as tiles that are neither of two colors.

Items are multiple choice with five answer choices, usually written as simplified fractions. Common traps include using permutations instead of combinations, confusing radius with area, and forgetting to exclude already counted categories.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

A 3-member committee is chosen randomly from 4 seniors and 3 juniors. What is the probability that the committee contains exactly 2 seniors and 1 junior?

Show answer

Answer: C — 1835\dfrac{18}{35}

There are (73)=35\binom{7}{3}=35 possible committees and (42)(31)=18\binom{4}{2}\binom{3}{1}=18 favorable committees. The probability is 1835\dfrac{18}{35}.

Question 2Easier

A circular flower bed with radius 6 feet lies entirely within a circular lawn with radius 10 feet. A point is selected at random from the lawn. What is the probability that the point is outside the flower bed?

Show answer

Answer: C — 1625\dfrac{16}{25}

The bed covers π(6)2=36π\pi(6)^2=36\pi of the lawn’s π(10)2=100π\pi(10)^2=100\pi square feet, so the point misses the bed with probability 100π−36π100π=1625\dfrac{100\pi-36\pi}{100\pi}=\dfrac{16}{25}.

Question 3Easier

A collection contains 28 ceramic tiles. Of these tiles, 9 are blue and 6 are green; all the remaining tiles are white. One tile will be randomly selected. What is the probability that the selected tile will be neither blue nor green?

Show answer

Answer: C — 1328\dfrac{13}{28}

There are 9+6=159+6=15 blue or green tiles, so 28−15=1328-15=13 tiles are neither color. The probability is therefore 1328\dfrac{13}{28}.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 57 Probability and sample spaces questions in the app

More ACT topics

Mathematics

Everything on the ACT

Study on the fly is an independent study tool and is not affiliated with, sponsored by, or endorsed by any testing organization, school, or government body.

ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, and does not endorse, this product.

All practice questions and passages are original works created for Study on the fly and are not reproduced from any official test.