CMClearMathAcademy

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

Why it matters: Weather forecasts, sports odds, board-game spinners, and lottery tickets all use probability. The chance is always between 0 and 1, or 0% and 100%.

Worked example

Problem. A bag has 3 red marbles and 5 blue marbles. What is the probability of choosing a red marble?

  1. There are 3 favorable outcomes: the red marbles.
  2. There are 8 total marbles.
  3. The probability is 3/8.
  4. Connect the calculation back to Probability Foundations so the method, not just the arithmetic, is clear.

Answer: 3/8

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. A fair coin is flipped once. What is the probability of heads?

Show solution
  1. There is 1 heads outcome out of 2 equally likely outcomes.
  2. The probability is 1/2.

Answer: 1/2

2. A number cube has faces 1 through 6. What is the probability of rolling a 4?

Show solution
  1. Only one face is a 4.
  2. There are 6 total faces.

Answer: 1/6

3. A bag has 2 green and 3 yellow tiles. What is the probability of choosing green?

Show solution
  1. There are 2 green tiles.
  2. There are 5 total tiles.

Answer: 2/5

4. A spinner has 8 equal sections and 3 are blue. What is the probability of blue?

Show solution
  1. There are 3 favorable sections out of 8 total.
  2. Probability is 3/8.

Answer: 3/8

5. A bag has 4 red and 6 black cards. What is the probability of choosing black?

Show solution
  1. There are 6 black cards out of 10 total.
  2. 6/10 simplifies to 3/5.

Answer: 3/5

Practice this interactively with instant feedback and an AI tutor.

Practice Probability Foundations Take the free placement check

More Pre-Algebra lessons