← Back to the Probability And Conditional Probability worksheet
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
Problem 1 Coin and Die Sample Space
(a) H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 (12 outcomes).
(b) Heads with 2, 4 or 6 gives 3 outcomes: 312 = 14.
(b) 1/4
Problem 2 Complement of an Event
P(on time) = 1 − P(late) = 1 − 0.18 = 0.82.
0.82 (82%)
Problem 3 Union and Intersection from Counts
Band only = 22 − 8 = 14. Robotics only = 17 − 8 = 9. Union = 14 + 8 + 9 = 31. Neither = 40 − 31 = 9.
P(band or robotics) = 3140 and P(neither) = 940.
31/40 and 9/40
Problem 4 Addition Rule
P(A ∪ B) = 0.45 + 0.30 − 0.12 = 0.63.
0.63
Problem 5 Test for Independence
P(A) · P(B) = 0.6 · 0.25 = 0.15, which equals P(A ∩ B).
Yes, independent
Problem 6 Conditional Probability from a Table
(a) 75 ÷ 150 = 0.5.
(b) Among 70 Grade 10 students, 29 buy lunch: 2970 ≈ 0.414.
(c) Among 75 who buy lunch, 29 are in Grade 10: 2975 ≈ 0.387.
(a) 0.5 (b) ≈ 0.414 (c) ≈ 0.387
Problem 7 Conditional Probability Formula
P(A | B) = 0.180.45 = 0.4.
0.4
Problem 8 Independence from Counts
P(instrument) = 48120 = 0.4. P(sport) = 75120 = 0.625. Product = 0.25.
P(both) = 30120 = 0.25, equal to the product.
Yes, independent
Problem 9 Free Throws in a Row
0.72 · 0.72 · 0.72 = 0.72³ = 0.373248.
≈ 0.373
Problem 10 Two Draws Without Replacement
P(red first) = 512. Given a red first, P(red second) = 411.
Product = 20132 = 533 ≈ 0.152.
5/33 ≈ 0.152
Problem 11 Medals for Eight Runners
Order matters: 8 · 7 · 6 = 336.
336 ways
Problem 12 Choosing a Committee
Order does not matter: ₁₁C₄ = 11 · 10 · 9 · 84 · 3 · 2 · 1 = 330.
330 committees
Problem 13 All-Girl Officers
Favorable: ₆C₃ = 20. Total: ₁₀C₃ = 120.
Probability = 20120 = 16.
1/6
Problem 14 Defective Parts
(a) 0.7(0.03) + 0.3(0.06) = 0.021 + 0.018 = 0.039.
(b) P(B | defective) = 0.0180.039 = 613 ≈ 0.462.
(a) 0.039 (b) 6/13 ≈ 0.462
Problem 15 Medical Test Result
Positive and sick: 0.02 · 0.95 = 0.019. Positive and healthy: 0.98 · 0.08 = 0.0784.
P(positive) = 0.0974. P(sick | positive) = 0.0190.0974 ≈ 0.1951.
≈ 19.5% (most positives are false alarms because the disease is rare).
Problem 16 Drawing Lots for a Trip
(a) Each volunteer has the same chance: 314 ≈ 0.214.
(b) ₁₄C₃ = 14 · 13 · 126 = 364.
(c) Every group of 3 is equally likely, so every volunteer has the same chance.
(a) 3/14 (b) 364 (c) equal chances for all
Problem 17 Is the Dice Game Fair?
Sum 7 has 6 outcomes and sum 11 has 2 outcomes out of 36: P(A) = 836 = 29 ≈ 0.222.
Then P(B) = 79. The chances are not equal.
Not fair; A scores with probability 2/9
Problem 18 Three Doors Strategy
(a) The first pick wins with probability 13 and stays the same.
(b) If the first pick was wrong (probability 23), the host reveals the other empty door and the remaining door must hold the prize. Switching wins with probability 23.
(a) 1/3 (b) 2/3, so switching is the better strategy
Problem 19 Raffle Tickets
Use the complement. P(none of his tickets win) = 115 · 114 · 113120 · 119 · 118 ≈ 0.8792.
Alternatively, ₁₁₅C₃ ÷ ₁₂₀C₃. So P(at least one) = 1 − 0.8792 ≈ 0.121.
≈ 0.121
Problem 20 Coffee and Pastry Orders
(a) 0.45 · 0.40 = 0.18.
(b) 0.45 + 0.30 − 0.18 = 0.57.
(c) 0.180.30 = 0.6.
(d) P(coffee) · P(pastry) = 0.45 · 0.30 = 0.135, which is not 0.18. Not independent.
(a) 0.18 (b) 0.57 (c) 0.6 (d) not independent