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Question

# Given 3 identical boxes I,II and III each containing two coins. In box I both are gold coins, in box II both are silver coins and in box III one is gold and 1 is silver. A coin is drawn from one of the boxes. If the coin is of gold, what is the probability that the other coin is the box is also of gold.(write answer up-to 2 decimal place)

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Solution

## Let B1: selecting box 1 having two gold coins.B2: selecting box 2 having two silver coinsB3: selecting box 3 having one gold & one silver.G: The second coin is of GoldWe need to find the probability that the other coin in the box is also of gold, if the first coin is of goldi.e., P(B1/G)P(B1/G)=P(B1)⋅P(G/B1)P(B1)⋅P(G/B1)+P(B2)⋅P(G/B2)+P(B3)P(G/B3)P(B1)=Probability of selecting box 1=1/3P(G/B1)= Probability that second coin is of gold in box 1=1P(B2)=Probabiluty of selecting box 2=1/3P(G/B2)=Probability that second coin is of gold in box 2=0P(B)3=Probability of selecting box 3=1/3P(G/B3)= Probability that second coin is of gold in box 3=1/2P(B1/G)=13×113×1+0×13+13×12=1313+16P(B1/G)=23.

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