Study Guide — Probability foundations

Probability

Undergraduate study guide for Probability foundations.

What this standard means

• Sample spaces, events, and axioms of probability
• Combinatorial probability: permutations and combinations
• Conditional probability and independence
• Bayes' theorem and law of total probability

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Draw a probability table or tree 2. Check probabilities sum to 1 3. Name the distribution before computing

_See printable PDF for diagram._

Common mistakes

• Assuming independence without justification
• Confusing P(A|B) and P(B|A)

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Probability foundations.

• [ ] Computes probabilities from models
• [ ] Finds expectation and variance
• [ ] Chooses appropriate distributions

Materials for this standard

• Practice Problems — 20 printable sets
• Review — 10 difficulty levels
• Practice Test — 10 difficulty levels
• Answer key — for parents and tutors