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Question

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king.


Solution

Total number of playing cards = 52
So the number of ways of drawing 1 card out of 52 cards =52
So n(S) = 52
(1) Drawn card is neither a heart nor a king
So probability of this can be obtained by (1- probability that the drawn card is heart or a king)
So total number of hearts = 13
Total number of kings = 4
and 1 card is both heart and king 
So P(heart or king) =P(heart)+P(king)-P(heart and king)
or P(heart or king)=13/52+4/52−1/52=16/52
So P(neither heart nor king)=1-P(heart or king)
=1−16/52=36/52=9/13−16/52=36/52=9/13

Mathematics

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