Study on the flyACTMathematicsProbability and sample spaces
Mathematics
Probability is the number of favorable outcomes divided by the total number of equally likely outcomes, and Probability and sample spaces is about counting both correctly.
Questions range from drawing a marble from a bag to choosing a committee, where combinations count the favorable and total groups. Complements save work: the chance of neither of two colors equals one minus the chance of either. Geometric probability also appears, comparing areas, such as the part of a large circle lying outside a smaller one.
Answer choices on ACT items are usually fractions, and distractors often come from forgetting to remove an item after drawing it or from counting an arrangement twice.
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?
Answer: C —
There are possible committees and favorable committees. The probability is .
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?
Answer: C —
The bed covers of the lawn’s square feet, so the point misses the bed with probability .
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?
Answer: C —
There are blue or green tiles, so tiles are neither color. The probability is therefore .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
Practice 61 Probability and sample spaces questions in the app
Harder than the exam: ACT Challenge · Competition-style problems
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