Compound Events Worksheets
Express probabilities as exact fractions, with assumptions about equally likely outcomes stated explicitly.
Before you begin
Read tables and graphs, count outcomes, and calculate with fractions.
Worked example
A bag contains 4 red and 7 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
- Replacement keeps the probabilities the same.
- Multiply the probabilities of the two independent draws.
Answer: 16/121
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
A bag contains 3 red and 4 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
2
A bag contains 5 red and 7 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
3
A bag contains 1 red and 4 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
4
A bag contains 7 red and 6 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
5
A bag contains 1 red and 6 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
6
A bag contains 6 red and 8 blue counters. Two counters are drawn at random, replacing the first before the second draw. What is the probability both are red?
Answer Key
1. 9/492. 25/1443. 1/254. 49/1695. 1/496. 9/49