← Back to the Probability Rules test
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)
0.55 + 0.35 − 0.20 = 0.70. Then 1 − 0.70 = 0.30. 0.70 and 0.30.
Scoring: 1 point for each.
Question 2 Independent or not (2 points)
0.25 × 0.8 = 0.20 equals P(A ∩ B), so they are independent. P(A | B) = 0.2/0.8 = 0.25, equal to P(A).
Scoring: 1 point for the decision with justification, 1 point for the conditional probability.
Question 3 Venn diagram of outdoor activities (3 points)
- (16 + 9)/60 = 5/12.
- Biking total = 21 + 9 = 30, so 9/30 = 3/10.
- 14/60 = 7/30.
Scoring: 1 point per part.
Question 4 Gym membership table (3 points)
- 67/150.
- 45/83.
- P(Weights) = 67/150 ≈ 0.447 but P(Weights | Morning) = 22/60 ≈ 0.367, so not independent.
Scoring: 1 point per part.
Question 5 Draws without replacement (2 points)
6/10 × 5/9 = 30/90 = 1/3.
Scoring: 1 point for the setup, 1 point for the result.
Question 6 Snow and a late bus (3 points)
- 0.4 × 0.6 + 0.6 × 0.1 = 0.24 + 0.06 = 0.30.
- P(snow | late) = 0.24/0.30 = 4/5.
Scoring: 1 point for (a), 1 point for the numerator, 1 point for the quotient.
Question 7 At least one success (2 points)
The complement is missing all three: 0.23 = 0.008. So P = 1 − 0.008 = 0.992.
Scoring: 1 point for the complement, 1 point for the answer.
Question 8 Conditional with dice (2 points)
Sum 9: (3,6), (4,5), (5,4), (6,3), 4 outcomes. With a 4: (4,5) and (5,4). 2/4 = 1/2.
Scoring: 1 point for the reduced sample space, 1 point for the answer.
Question 9 Exclusive versus independent (1 point)
No. Exclusive events have P(A ∩ B) = 0, but independence needs P(A)P(B) > 0.
Scoring: 1 point for the answer with a reason.