Question

A card is down & replaced in ordinary pack of 52 playing cards. Minimum number of times must a card be drawn so that there is atleast an even chance of drawing a heart, is

• A. $2$
• B. $3$
• C. $4$
• D. more than four

Answer 1

The correct option is A $2$

Probability of drawing a heat in one draw $=\frac{1}{4}$

For $n$ drawing Probability of not getting any heat $=\frac{3}{4}$

$\therefore$ Probability of drawing at least one heat

$1-(\frac{3}{4}{)}^n$

By addition

$1-(\frac{3}{4}{)}^n\ge \frac{1}{2}$

$\Rightarrow (\frac{3}{4}{)}^n\le \frac{1}{2}$

$\Rightarrow \left(log\frac{3}{4}\right)\le log\frac{1}{2}$

$\Rightarrow n\le \frac{log\frac{1}{2}}{log\frac{3}{4}}$

$\Rightarrow n\le 2.4$

$\therefore n=2$