Chapter 14: Probability Rules

What is the General Addition Rule?

For any two events A and B:

  P(A or B) = P(A) + P(B) − P(A and B)

Use this rule when events are not disjoint.

What is a conditional probability?

The probability of event B given event A:

  P(B | A) = P(A and B) / P(A)

It focuses only on outcomes where A has occurred.

What does it mean for events to be independent?

Events A and B are independent if:

  P(B | A) = P(B)

  (or equivalently, P(A and B) = P(A) × P(B))

Can disjoint events be independent?

No. Disjoint events cannot be independent because if one occurs, the other cannot.

Knowing one happened affects the chance of the other.

What’s the danger of assuming independence or disjoint events?

You might incorrectly apply the Multiplication or Addition Rules.

Always check whether events meet the conditions.

What is the General Multiplication Rule?

P(A and B) = P(A) × P(B | A)

Use when events are not independent

What is sampling without replacement?

Once an individual is chosen, it’s not returned to the pool.

This changes probabilities and creates conditional probability.

What is a tree diagram used for?

To visualize sequences of events and conditional probabilities.

Each path represents a unique outcome; all final probabilities add to 1.

Why is reversing the conditioning tricky?

Knowing P(B | A) doesn’t automatically give you P(A | B).

You need additional info (like Bayes’ Theorem or joint probabilities).

What tools can help solve probability problems?

• Venn Diagrams

• Contingency Tables (2-way tables)

• Tree Diagrams

What’s a key AP Statistics tip for probability problems?

• Always check for independence or disjointness

• Read conditional probabilities carefully

• Practice with 2-way tables for conditional and joint probability