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A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

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Let E1 : the event that lost cards is a diamond ⇒ n(E1) = 13 

E2 : lost cards is not a diamond n(E2) = 52 – 13 = 39 

And, n(S) = 52 

Then, E1 and E2 are mutually exclusive and exhaustive events.

∴ P(E1) = 13/52 = 1/4 and P(E2) = 39/52 = 3/4

Let E : the events that two cards drawn from the remaining pack are diamonds, When one diamond card is lost, there are 12 diamond cards out of 51 cards. The cards can be drawn out of 12 diamond cards in 12C2 ways.

Similarly, 2 diamond cards can be drawn out of 51 cards in 51C2 ways. The probability of getting two cards, when one diamond card is lost, is given by P(E/E1)

By using Baye’s theorem, we obtain

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