A fair six-sided die is rolled once.
Let: \[A=\{2,4,6\},\qquad B=\{1,2,3,4\}.\]

Question

Calculate $P(A)$, $P(B)$, and $P(A\cap B)$.
Use a calculation to decide whether $A$ and $B$ are independent.
Are they mutually exclusive? Explain.
Explain why “independent events must come from separate experiments” is false.

Accepted Answer

(a) $\frac{1}{2}$, $\frac{2}{3}$, $\frac{1}{3}$; (b) Independent; (c) Not mutually exclusive; (d) Independence concerns probabilities, not the number of experiments.

Probability

Probability

Solution:

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