Mathematics

Problem

A fair die is rolled once. Define events

A=\{\text{‘the outcome is even’}\}

and

B=\{\text{‘the outcome is prime’}\}

. Which of the following describes the relationship between

A

and

B

? a) Both mutually exclusive and independent b) Neither mutually exclusive nor independent c) Independent but not mutually exclusive d) Mutually exclusive but not independent

Intuitive explanation

The key is to identify which outcomes belong to each event, then check whether knowing one tells you anything about the other. Event $A$ contains the even numbers {2, 4, 6}, while event $B$ contains the primes {2, 3, 5}—they overlap only at 2. Two events are independent if the probability of both happening equals the product of their individual probabilities; if not, they're dependent. Calculate $P(A)$ , $P(B)$ , and $P(A \cap B)$ to see which relationship holds.

Intuitive explanation

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