Question:
Two cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If drawn card is diamond, find the probability that the lost cards were both hearts.
Answer:
Total number of cards = 52
Two cards are lost.
So remaining cards = 50
Now one card is drawn.
Probability that it is a diamond card = 13/50
Now probability that both lost cards are heart = 13/50 *( 11C2 / 49C2 )
= 13/50 *[{(11*10)/2}/{(49*48/2)}]
= 13/50 *{(11*10)/(49*48)}
= {(13*11*10)/(50*49*48)}
= {(13*11)/(5*49*48)}
= 143/11760
So probability that both lost card are heart = 143/11760
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