Practice Dependence (Statistical) in Math

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

Quick Recap

When the probability of one event changes based on whether another event occurred.

Knowing A happened tells you something about B—they're connected.

Example 1

medium
A bag has 5 red and 3 blue balls. Two balls are drawn without replacement. Find P(\text{both red}) using the multiplication rule for dependent events.

Example 2

hard
Disease test: P(\text{disease}) = 0.05. Test positive given disease: P(+|D) = 0.90. Test positive given no disease: P(+|D^c) = 0.10. Find P(D \cap +) and P(D^c \cap +).

Example 3

easy
A deck of 52 cards. Find P(\text{drawing two aces in a row}) without replacement.

Example 4

hard
Verify whether smoking and lung cancer are dependent using the following: P(\text{cancer}) = 0.06, P(\text{cancer}|\text{smoker}) = 0.15. What does this tell us about the relationship?
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