← Back to the Probability And Conditional Probability 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, S-CP.B.8, S-CP.B.9, S-MD.B.6, S-MD.B.7 · Level: Grade 10 Geometry
Question 1 Two Dice (2 points)
Sums of 10, 11 and 12 occur in 3 + 2 + 1 = 6 outcomes out of 36: 636 = 16.
Complement: 1 − 16 = 56.
1/6 and 5/6
Scoring: 1 point each.
Question 2 Venn Counts (3 points)
(a) 28 + 22 − 9 = 41, so 4160.
(b) 60 − 41 = 19, so 1960.
(c) 928 ≈ 0.321.
(a) 41/60 (b) 19/60 (c) 9/28
Scoring: 1 point per part.
Question 3 Two-Way Table (3 points)
(a) 95200 = 0.475.
(b) 73120 ≈ 0.608.
(c) 58105 ≈ 0.552.
(a) 0.475 (b) ≈ 0.608 (c) ≈ 0.552
Scoring: 1 point per part; award the point only if the denominator is the condition total.
Question 4 Independent or Not? (2 points)
P(A ∩ B) = 0.5 + 0.4 − 0.7 = 0.2.
0.5 · 0.4 = 0.2, equal to P(A ∩ B).
0.2; independent
Scoring: 1 point for the intersection, 1 point for the independence check.
Question 5 Orders and Groups (2 points)
(a) Order matters: 7 · 6 · 5 = 210.
(b) Order does not matter: ₇C₃ = 210 ÷ 6 = 35.
(a) 210 (b) 35
Scoring: 1 point each.
Question 6 Marbles Without Replacement (3 points)
(a) 615 · 514 = 30210 = 17.
(b) Green then yellow: 615 · 914 = 54210. Yellow then green: 915 · 614 = 54210. Total 108210 = 1835.
(a) 1/7 (b) 18/35
Scoring: 1 point for (a), 2 points for (b).
Question 7 A Positive Test (3 points)
Sick and positive: 0.04 · 0.9 = 0.036. Healthy and positive: 0.96 · 0.1 = 0.096.
P(positive) = 0.132. P(sick | positive) = 0.0360.132 = 311 ≈ 0.273.
3/11 ≈ 27.3%
Scoring: 1 point for each of the two paths, 1 point for the conditional probability.
Question 8 Fair Spinner Game (2 points)
First game: each player wins with probability 24 = 12. Fair.
Second game: Ben wins with probability 14 and Anna with 34. Not fair.
First fair; second not fair
Scoring: 1 point for each game.