Q. A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he fail the first two times is
A) $\frac{9}{64}$
B) $\frac{1}{64}$
C) $\frac{1}{16}$
D) $\frac{9}{16}$
Explanation
(d)
Total number of cards =52
$Probability\ of\ getting\ spade = \frac{13}{52} = \frac{1}{4}$
$Probability\ of\ not\ getting\ spade = 1 - \frac{1}{4} = \frac{3}{4}$
$\therefore Required\ probability = \frac{3}{4} \bullet \frac{3}{4} = \frac{9}{16}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.