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A box contains 2 gold and 3 silver coins...

A box contains 2 gold and 3 silver coins. Another box contains 3 gold and 3 silver coins. A box is chosen at random, and a coin is drawn from it. If the selected coin is a gold coin, find the probability that it was drawn from the second box.

Text Solution

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P(A)=P(B)=1/2
A->2G,3S
B->3G,3S P(G/A)=2/5,P(G/B)=1/2
`P(G)=1/2*2/5+1/2*1/2=9/20`
`P(B|G)=(P(B)*P(G|B))/(P(G)`
`=(1/2*1/2)/(4/20)=5/9`.
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