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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.

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913

313

713

answer is A.

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Detailed Solution

Given: A card is drawn at random from a pack of 52 cards.
So, the total number of outcomes is, n(S) = 52.
The probability of an event is given by,

Pr o b a b i l i t y = Number of favourable outcomes Total number of outcomes

Let A be the required event of drawing neither a heart nor the king.
There are 13 hearts and 3 kings (other than that of hearts). Therefore, the number of favourable outcomes is given by,

n (A) = 52 − 13 − 3 ⇒ n (A) = 52 − 16 ⇒ n (A) = 36

Find the probability of drawing neither a heart nor a king is given by,

P (A) = n (A) n (S) ⇒ P (A) = 3652 ⇒ P (A) = 913

So, the probability of drawing a card neither a king nor a heart is

913

. So, the correct option is 1.

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