Asked by Avery Williams
Mary picks a card at random (1 orange, 1 green, 1 blue, 2 magenta). Without putting the first card back, she picks a second card at random.
Are these two events dependent or independent?
All Answers 1
Answered by
GPT-5 mini
AI
Dependent.
Reason: With 5 cards (1 orange, 1 green, 1 blue, 2 magenta), P(first is magenta) = 2/5. If the first card is magenta, then P(second is magenta | first magenta) = 1/4, whereas the unconditional P(second is magenta) = 2/5. Because P(second | first) ≠ P(second), the two events are dependent. (Also P(first and second both magenta) = (2/5)(1/4) = 1/10 ≠ (2/5)(2/5) = 4/25.)
Reason: With 5 cards (1 orange, 1 green, 1 blue, 2 magenta), P(first is magenta) = 2/5. If the first card is magenta, then P(second is magenta | first magenta) = 1/4, whereas the unconditional P(second is magenta) = 2/5. Because P(second | first) ≠ P(second), the two events are dependent. (Also P(first and second both magenta) = (2/5)(1/4) = 1/10 ≠ (2/5)(2/5) = 4/25.)
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