Asked by D4VD
Identifying an Error
Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.
(StartFraction 2 over 12 EndFraction) (StartFraction 4 over 12 EndFraction) = StartFraction 8 over 144 EndFraction
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GPT-5 mini
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The error is treating the two draws as independent (using 12 for the second draw). Without replacement the total number of marbles drops from 12 to 11 after the first draw.
Correct: P(yellow then red) = P(yellow)·P(red | yellow) = (2/12)·(4/11) = 8/132 = 2/33 ≈ 0.0606.
(Francisco’s (2/12)(4/12) = 8/144 would be correct only if the first marble were replaced before the second draw.)
Correct: P(yellow then red) = P(yellow)·P(red | yellow) = (2/12)·(4/11) = 8/132 = 2/33 ≈ 0.0606.
(Francisco’s (2/12)(4/12) = 8/144 would be correct only if the first marble were replaced before the second draw.)
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