Question

5 cards are drawn one after an other successively with replacement from a well shuffled pack of 52 cards. The probability that none is a spade is

• A. 1-$(\frac{3}{4}{)}^5$
• B. $(\frac{3}{4}{)}^5$
• C. $(\frac{1}{4}{)}^5$
• D. 1-$(\frac{1}{4}{)}^5$

Answer 1

The correct option is B $(\frac{3}{4}{)}^5$

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)
When we draw 5 cards from a card and none is a spade with replacement $=(\frac{3}{4}{)}^5$