Question

5 cards are drawn one after an other successively with replacement from a well shuffled pack of 52 cards. The probability that all the 5 cards are spades

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

Answer 1

Answer: (C)

${\left(\frac{1}{4}\right)}^5$

Probability when one card drawn from a card pack of 52 and that is a spade is $=\frac{13}{52}=\frac{1}{4}$ (There are 13 spade cards in a pack of 52 cards)
When we draw 5 cards from a card and that all are spade with replacement $=(\frac{1}{4}{)}^5$