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November 6th, 2017, 07:43 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, 08:37 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,093 Thanks: 1087 
There are two boxes, label the one w/2 gold coins $GG$ and the one with one gold, one silver coin $GS$ $P[GG] = P[GG \wedge GS]P[GS] + P[GG \wedge GG]P[GG] = (0)(1/2) + (1)(1/2) = 1/2$ 
November 6th, 2017, 12:47 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,583 Thanks: 610 
Number the coins 14, 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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