Given three identical boxes I, II and III, each containing two coins. In ox I both coins are gold coins, in box II both are silver coins and in box III there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?

Explanation

`B_{1}` choosed box (I) have two gold coins,


`B_{2}` :choosed box II having two silver coins,


`B_{3}` :choosed III having one silver and one gold coin,


G: = shows Coin is gold.



`P(B_{1})=P(B_{2})=P(B_{3})=frac{1}{3} `


`P(frac{G}{B_{1}})=1, P(frac{G}{B_{2}})=0, P(frac{G}{B_{3}})=frac{1}{2} `


`P(G)=P(B_{1}) P(frac{G}{B_{1}})+P(B_{2}) P(frac{G}{B_{2}})+P(B_{3}. `


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