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AP STATISTICS · PROBABILITY

Probability Rules

Addition, multiplication, and conditional probability — the grammar of chance.

15 min read 3 practice questions
Probability measures how likely an event is, from 00 (impossible) to 11 (certain). Three rules carry you through most AP problems.
P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)

General addition rule

P(A∩B)=P(A)⋅P(B∣A)P(A \cap B) = P(A)\cdot P(B \mid A)

General multiplication rule

P(B∣A)=P(A∩B)P(A)P(B \mid A) = \frac{P(A \cap B)}{P(A)}

Conditional probability

Events are independent if knowing one occurred doesn't change the probability of the other: P(B∣A)=P(B)P(B \mid A) = P(B). Events are mutually exclusive if they can't happen together: P(A∩B)=0P(A \cap B) = 0.

Worked example · Two independent events

A free-throw shooter makes 80%80\% of shots. Assuming independence, what's the probability she makes two in a row?
  1. 1
    P(make, make)=0.8×0.8P(\text{make, make}) = 0.8 \times 0.8.
  2. 2
    =0.64= 0.64.

CHECK YOUR UNDERSTANDING

Practice

Answer each question, then check.

1
P(A)=0.5P(A) = 0.5, P(B)=0.4P(B) = 0.4, P(A∩B)=0.2P(A \cap B) = 0.2. Find P(A∪B)P(A \cup B).
2
P(A)=0.6P(A) = 0.6 and P(A∩B)=0.15P(A \cap B) = 0.15. Find P(B∣A)P(B \mid A).
3
P(A)=0.3P(A) = 0.3, P(B)=0.5P(B) = 0.5, P(A∩B)=0.15P(A \cap B) = 0.15. Are AA and BB independent?

Numeric answers accept decimals or fractions like 3/4.