Baye's Theorem Example 2

There are three identical boxes A, B and C  each having two coins.

In box A, both are gold coins.

In box B, both are silver coins.

In box C, one is gold other is a sliver.

If a coin is picked up and found to be gold. Find the probability that the other coin in the box is gold.




They are saying to find the probability that other coins is also gold.  this is possible only when box A is selected because it contains two gold coins. So this question can be also asked as "find the probability that gold coin is drawn from bag A".

We have to find out P(A/ G) =?

P(A/G) = P(A∩ G) / P(G) or

              ={ P(A). P(G/A) } / P(G)

Probabilty of choosing a bag is 1/3 beacuse there are 3 bags and all are identical

P(G)= P(A).P(G/A) + P(B).P(G/B) + P(C).P(G/C)

          = (1/3). (1) + (1/3)(0) + (1/3)(1/2)

         =   1/2 

P(A). P(G/A) = 1/3

P(A/ G) = (1/3) / (1/2)= 2/3