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November 6th, 2017, 08:43 AM   #1
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Probability problem

I need help with my homework problem:

Suppose there are two closed boxes. In each box are two coins; one box contains two gold coins, the other contains one gold coin and one silver coin. A coin will be drawn from one of these two boxes. Assume that each box has an equal chance of being chosen, and that within each box, each coin has an equal chance of being chosen. When the coin is drawn, it turns out to be gold. What is the probability that the other coin in the same box is gold?
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November 6th, 2017, 09:37 AM   #2
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There are two boxes, label the one w/2 gold coins $GG$ and the one with one gold, one silver coin $GS$

$P[G|G] = P[G|G \wedge GS]P[GS] + P[G|G \wedge GG]P[GG] = (0)(1/2) + (1)(1/2) = 1/2$
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November 6th, 2017, 01:47 PM   #3
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Number the coins 1-4, where 1 and 2 are gold in box 1, while 3 is gold in box 2 and 4 is silver in box 2.
choose 1 other is gold
choose 2 other is gold
choose 3 other is silver
choose 4 - not gold

Net result - probability other coin is gold is 2/3.
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