Question

A card is drawn and replaced in an ordinary set of 52 cards.Minimum number of times a card must be drawn so that there is atleast an even chance of drawing a heart?

• A. 1
• B. 3
• C. 4
• D. 2

Answer 1

The correct option is B

3

Even chance means the probability is $\frac{1}{2}$.Let S denotes probability of success and F for failure.

$P\left(E\right)=P(SorFSorFFSorFFFS....nterms)$

$P\left(S\right)=\frac{1}{4}$

$P\left(F\right)=\frac{3}{4}$

$P\left(E\right)=P\left(S\right)\frac{\left[P\right(F{)}^{n-1}]}{\left[P\right(F)-1]}$

$P\left(E\right)=1-{\frac{3}{4}}^n\le \frac{1}{2}$

$n_{min}=3$