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A card is picked at random from a pack of cards. Given that the picked card is a queen, what is the probability that it is a spade?
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The correct answer is:
$\frac{1}{4}$
Let $A$ be the event that a card is queen and $B$ be the event that it is a spade.
Now, $P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 52}{4 / 52}=\frac{1}{4}$
Now, $P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 52}{4 / 52}=\frac{1}{4}$
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