Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7 · Level: Grade 11 Algebra 2
Question 1 Union and complement (2 points)
A town survey finds that 55% of residents recycle, 35% compost, and 20% do both. Find the probability that a resident recycles or composts, and the probability that a resident does neither.
Question 2 Independent or not (2 points)
For event A (a student walks to school) and event B (a student lives within a mile), P(A) = 0.25, P(B) = 0.8 and P(A ∩ B) = 0.2. Are A and B independent? Find P(A | B).
Question 3 Venn diagram of outdoor activities (3 points)
Of 60 people, the diagram shows how many hike only, bike only, do both, or do neither.
- Find P(hiking). (1 point)
- Find P(hiking | biking). (1 point)
- Find P(neither). (1 point)
Question 4 Gym membership table (3 points)
A gym has 150 members. The table shows when they work out and what they mainly do.
- Find P(Weights). (1 point)
- Find P(Evening | Cardio). (1 point)
- Are “Weights” and “Morning” independent? Justify. (1 point)
Question 5 Draws without replacement (2 points)
A box has 4 green and 6 yellow cubes. Two are drawn without replacement. Find the probability that both are yellow.
Question 6 Snow and a late bus (3 points)
The probability of snow is 0.4. When it snows the bus is late with probability 0.6, and when it does not snow the bus is late with probability 0.1.
- Find P(late). (1 point)
- Given the bus is late, find P(snow) as a fraction. (2 points)
Question 7 At least one success (2 points)
An archer hits the target 80% of the time, and shots are independent. Find the probability of at least one hit in three shots.
Question 8 Conditional with dice (2 points)
Two fair dice are rolled. Given that the sum is 9, find the probability that at least one die shows a 4.
Question 9 Exclusive versus independent (1 point)
Can two mutually exclusive events, each with positive probability, be independent? Explain in one sentence.
