Box-I contains 2 gold coins, while another Box-II contains 1 gold and 1 silver coin. A person choose a box at random and takes out a coin. If the coin is of gold, what is the probability that the order coin in the box is also of gold?
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Solution
Let E1 and E2 be the events that the boxes I and II are chosen respectively.
⟹P(E1)=12=P(E2)
Let A be the event that the coin drawn is of gold.
⟹P(A|E1)=P(a gold coin from box I)=22=1
P(A|E2)=P(a gold coin from box II)=12
Probability that the other coin in the box is of gold = The probability that the gold coin is drawn from box I=P(E1|A)