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 coin is flipped and a six-sided die is rolled. (a) List the sample space. (b) Find P(heads and an even number).
Problem 2 Complement of an Event ★★★
The school bus is late on 18% of mornings. Find the probability that it is on time on a randomly chosen morning, and write the complement rule you used.
Problem 3 Union and Intersection from Counts ★★★
Of 40 students, 22 are in band, 17 are in robotics, and 8 are in both. Find P(band or robotics) and P(neither club).
Problem 4 Addition Rule ★★★
For two events, P(A) = 0.45, P(B) = 0.30 and P(A ∩ B) = 0.12. Find P(A ∪ B).
Problem 5 Test for Independence ★★★
Events A and B have P(A) = 0.6, P(B) = 0.25 and P(A ∩ B) = 0.15. Are they independent?
Problem 6 Conditional Probability from a Table ★★★
| Grade 9 | Grade 10 | Total | |
|---|---|---|---|
| Brings lunch | 34 | 41 | 75 |
| Buys lunch | 46 | 29 | 75 |
| Total | 80 | 70 | 150 |
One student is chosen at random from the table. Find (a) P(buys lunch), (b) P(buys lunch | Grade 10), (c) P(Grade 10 | buys lunch). Round to the nearest thousandth where needed.
Problem 7 Conditional Probability Formula ★★★
Given P(A ∩ B) = 0.18 and P(B) = 0.45, find P(A | B).
Problem 8 Independence from Counts ★★★
Of 120 students, 48 play an instrument, 75 play a sport, and 30 do both. Are playing an instrument and playing a sport independent? Justify with numbers.
Problem 9 Free Throws in a Row ★★★
A basketball player makes 72% of her free throws, and each shot is independent. What is the probability that she makes three in a row, to the nearest thousandth?
Problem 10 Two Draws Without Replacement ★★★
A bag holds 5 red marbles and 7 blue marbles. Two marbles are drawn without replacement. Find the probability that both are red.
Problem 11 Medals for Eight Runners ★★★
Eight runners reach a final. In how many ways can gold, silver and bronze be given out?
Problem 12 Choosing a Committee ★★★
A club with 11 members elects a committee of 4. How many different committees are possible?
Problem 13 All-Girl Officers ★★★
Three officers are chosen at random from a group of 6 girls and 4 boys. Find the probability that all three are girls.
Problem 14 Defective Parts ★★★
Machine A makes 70% of a factory’s parts and 3% of them are defective. Machine B makes 30% and 6% are defective. (a) Find P(a random part is defective). (b) Given a defective part, find the probability that it came from machine B.
Problem 15 Medical Test Result ★★★
A disease affects 2% of a population. A screening test is positive for 95% of people who have the disease and for 8% of people who do not. A person tests positive. Find the probability that the person actually has the disease, to the nearest tenth of a percent.
Problem 16 Drawing Lots for a Trip ★★★
Fourteen volunteers want to attend a robotics event and 3 may go. Names are drawn at random. (a) What is the probability that a particular volunteer is chosen? (b) How many different groups of 3 are possible? (c) Explain why drawing names is a fair method.
Problem 17 Is the Dice Game Fair? ★★★
Two players roll two dice. Player A scores when the sum is 7 or 11. Player B scores on any other sum. Is the game fair? If not, find the probability that A scores.
Problem 18 Three Doors Strategy ★★★
A prize is hidden behind one of three doors. A contestant picks door 1. The host, who knows where the prize is, opens another door that has no prize and offers a switch. Find the probability of winning (a) by staying and (b) by switching.
Problem 19 Raffle Tickets ★★★
A raffle has 120 tickets and 3 different prizes are drawn without replacement. Marcus holds 5 tickets. Find the probability that he wins at least one prize, to the nearest thousandth.
Problem 20 Coffee and Pastry Orders ★★★
At a cafe, 45% of customers buy coffee and 30% buy a pastry. Of the coffee buyers, 40% also buy a pastry. Find (a) P(coffee and pastry), (b) P(coffee or pastry), (c) P(coffee | pastry), and (d) decide whether the two purchases are independent.
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