Common Mistakes

Statistics · AP · Probability, Random Variables, and Probability Distributions

Focus

Independent Events and Unions of Events

This topic is assessed on the AP Exam.

Frequent mistakes

### 1. P(A|B) vs P(A and B)

What it looks/sounds like: Conditional probability uses the wrong formula.

Why it happens: Independence is assumed without checking.

How to fix: Write P(A|B) = P(A∩B)/P(B); verify independence if claimed.

### 2. Binomial misidentification

What it looks/sounds like: Binomial formula used when trials are not independent/fixed n.

Why it happens: Settings are not checked.

How to fix: Confirm fixed n, two outcomes, constant p, independent trials.

### 3. Correct work, wrong question

What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.

Why it happens: Attention locks onto the first operation instead of the final ask.

How to fix: Underline the final question; after solving, verify the boxed answer matches it.

### 4. Notation and justification gaps

What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.

Why it happens: Notation is treated as decoration rather than part of the score.

How to fix: Add one justification phrase per major step (definition, theorem, or rule).

How to avoid them

1. Define the random variable and its distribution. 2. Check probabilities are valid. 3. Interpret expected value in context.

Quick self-check

• [ ] Can compute a conditional probability
• [ ] Can identify a binomial setting
• [ ] Can interpret expected value