Probability Foundations
A free Pre-Algebra lesson from the “Statistics and Probability” unit, with a worked example and practice problems including step-by-step solutions.
Probability describes how likely an event is. For equally likely outcomes, probability is favorable outcomes divided by total outcomes. A probability of 0 means impossible, 1 means certain, and values between 0 and 1 describe events that might happen. In Statistics and Probability, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Find simple probabilities
- Use fractions to describe chance
- Use complements and sample spaces
Worked example
Problem. A bag has 3 red marbles and 5 blue marbles. What is the probability of choosing a red marble?
- There are 3 favorable outcomes: the red marbles.
- There are 8 total marbles.
- The probability is 3/8.
- Connect the calculation back to Probability Foundations so the method, not just the arithmetic, is clear.
Answer: 3/8
Practice problems
1. A fair coin is flipped once. What is the probability of heads?
Show solution
- Warm-up: First identify exactly what the question is asking: A fair coin is flipped once. What is the probability of heads?
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- There is 1 heads outcome out of 2 equally likely outcomes.
- The probability is 1/2.
- Check the result by substituting or estimating: the response should match 1/2 and make sense in the original problem.
Answer: 1/2
2. A number cube has faces 1 through 6. What is the probability of rolling a 4?
Show solution
- Warm-up: First identify exactly what the question is asking: A number cube has faces 1 through 6. What is the probability of rolling a 4?
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- Only one face is a 4.
- There are 6 total faces.
- Check the result by substituting or estimating: the response should match 1/6 and make sense in the original problem.
Answer: 1/6
3. A bag has 2 green and 3 yellow tiles. What is the probability of choosing green?
Show solution
- Warm-up: First identify exactly what the question is asking: A bag has 2 green and 3 yellow tiles. What is the probability of choosing green?
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- There are 2 green tiles.
- There are 5 total tiles.
- Check the result by substituting or estimating: the response should match 2/5 and make sense in the original problem.
Answer: 2/5
4. A spinner has 8 equal sections and 3 are blue. What is the probability of blue?
Show solution
- Core Practice: First identify exactly what the question is asking: A spinner has 8 equal sections and 3 are blue. What is the probability of blue?
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- There are 3 favorable sections out of 8 total.
- Probability is 3/8.
- Check the result by substituting or estimating: the response should match 3/8 and make sense in the original problem.
Answer: 3/8
5. A bag has 4 red and 6 black cards. What is the probability of choosing black?
Show solution
- Core Practice: First identify exactly what the question is asking: A bag has 4 red and 6 black cards. What is the probability of choosing black?
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- There are 6 black cards out of 10 total.
- 6/10 simplifies to 3/5.
- Check the result by substituting or estimating: the response should match 3/5 and make sense in the original problem.
Answer: 3/5
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