Question

A card is drawn and replaced three times from an ordinary pack of 52 playing cards. The probability that atleast one spade is drawn is

• A. $\frac{9}{64}$
• B. $\frac{1}{64}$
• C. $\frac{37}{64}$
• D. $\frac{3}{64}$

Answer 1

The correct option is C $\frac{37}{64}$

Probability when one card drawn from a card pack of 52 and not a spade is $=1-\frac{13}{52}=\frac{3}{4}$ (There are 13 spade cards in a pack of 52 cards)
Probability of atleast one spade is drawn $=$ 1 $-$ Probability that none of the three is spade
$=1-(\frac{3}{4}{)}^3=\frac{37}{64}$