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Question

A card is selected at random from well-shuffled pack of 52 cards. Find the probability that the selected card is
(1) a black coloured queen.
(2) not a king.

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Solution

For the given experiment, the number of equally likely outcomes is 52
n=52
(i) Let A be the event that the selected card is a black coloured queen.
The number of favourable outcomes is 2 (i.e., queen of spade or club)
P(A)=252=126
(ii) Let B be the event that the selected card is a king. The number of favourable outcomes is 4 as there contains 4 kings in a pack of 52 cards.
P(B)=452=113
Then B is the event that the selected card is not king.
Then, P(B)=1P(B)=1113=1213
Hence, the answer is 1213.

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