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.
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.
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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