Question

A person draws a card from a pack, replaces it shuffles the pack, again draws a card, replace it and draws again. This process he does until he draw a heart card. The probability that he will have to make at least four draws is

• A. $\frac{27}{256}$
• B. $\frac{17}{256}$
• C. $\frac{27}{64}$
• D. $\frac{27}{16}$

Answer 1

The correct option is C $\frac{27}{64}$

P(getting a heart card) $=\frac{1}{4}$
Therefore required probability = ${\left(\frac{3}{4}\right)}^3\frac{1}{4}+{\left(\frac{3}{4}\right)}^4\frac{1}{4}{\left(\frac{3}{4}\right)}^5\frac{1}{4}+...\frac{{\left(\frac{3}{4}\right)}^5\frac{1}{4}}{1-\frac{3}{4}}=\frac{27}{64}$