My Math Forum Probability problem

 November 6th, 2017, 08:43 AM #1 Newbie   Joined: Nov 2017 From: San Diego, CA Posts: 1 Thanks: 0 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?
 November 6th, 2017, 09:37 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,197 Thanks: 1152 There are two boxes, label the one w/2 gold coins $GG$ and the one with one gold, one silver coin $GS$ $P[G|G] = P[G|G \wedge GS]P[GS] + P[G|G \wedge GG]P[GG] = (0)(1/2) + (1)(1/2) = 1/2$
 November 6th, 2017, 01:47 PM #3 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 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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