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  4. 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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Q. 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 ?

COMEDKCOMEDK 2014Probability - Part 2

Solution:

Let $A$ be the event that a card is queen and $B$ be the event that it is a spade.
Now, $P(B|A) = \frac{P(B\, \cap \,A)}{P(A)} = \frac{1 /52}{4/52} = \frac{1}{4}$