Question
A shuffled set contains eight distinct cards: green cards numbered 1 through 5 and yellow cards numbered 1 through 3. Draw one card at random. Let G mean the drawn card is green and E mean its number is even.
(a) Enumerate the sample space.
(b) Find P(G).
(c) Find P(G|E).
(d) Find P(G AND E).
(e) Find P(G OR E).
(f) Decide whether G and E are mutually exclusive and justify with a numerical probability.
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Evidence boundary
This is OpenStax Introductory Statistics, chapter 3 Homework exercise 85, with all six parts and the original G/E event definitions. The probabilities assume the stated well-shuffled random single draw, giving each distinct colored and numbered card probability 1/8. These are exact model probabilities, not empirical frequencies from repeated draws.