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Question

A card from a deck of 52 cards is lost. From the remaining cards, two cards are drawn with replacement and found to be clubs, then the probability that

A
missing card is a club is 16523
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B
missing card is a spade is 1351
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C
missing card is a spade is 14
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D
missing card is a club is 14
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Solution

The correct option is C missing card is a spade is 14
Let
E1: missing card is a club
E2: missing card is other than club
E : drawn cards are club

P(E1|E)=P(E|E1)P(E1)P(E|E1)P(E1)+P(E|E2)P(E2)

P(E1|E)=(1251)2×14(1251)2×14+(3951)2×34 =16523

Probability of lost card being spades is 14

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