Practice Compound Probability in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The probability of two or more events occurring together (P(A \text{ and } B)) or at least one occurring (P(A \text{ or } B)), accounting for whether the events are independent or dependent.

Single-event probability asks about one thing happening. Compound probability asks about combinations: 'What's the chance of rolling a 6 AND flipping heads?' or 'What's the chance of drawing a heart OR a face card?' The word 'and' usually means multiply; the word 'or' usually means add (but subtract the overlap).

Example 1

medium
Events A and B: P(A)=0.5, P(B)=0.4, P(A \cap B)=0.2. Find (a) P(A \cup B), (b) P(A|B), and verify whether A and B are independent.

Example 2

hard
A card is drawn from a standard deck. Event A: card is red. Event B: card is a face card (J, Q, K). Find P(A \cup B) and P(A \cap B).

Example 3

easy
P(A)=0.3, P(B)=0.5, and A and B are mutually exclusive. Find P(A \cup B).

Example 4

hard
Using the law of total probability: P(B) = P(B|A)P(A) + P(B|A^c)P(A^c), find P(B) given P(A)=0.4, P(B|A)=0.7, P(B|A^c)=0.3.
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