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  • A man draws a card from a pack of 52 cards and then replaces it. After shuffling the pack, he again draws a card. This he repeats a number of times. The probability that he will draw a heart for th

A man draws a card from a pack of 52 cards and then replaces it. After shuffling the pack, he again draws a card. This he repeats a number of times. The probability that he will draw a heart for the first time in the third draw is

Option: 1

\frac{9}{64}


Option: 2

\frac{27}{64}


Option: 3

\mathrm{\frac{1}{4} \times \frac{{ }^{39} C_2}{{ }^{52} C_2}}


Option: 4

None of these


Answers (1)

best_answer

Let E= the event of drawing a heart. Clearly, \mathrm{P(E)=\frac{{ }^{13} C_1}{{ }^{52} C_1}=\frac{1}{4}}
\begin{aligned} \therefore \text { the required probability } & = \mathrm{P(\bar{E} \bar{E} E)=P(\bar{E}) \cdot P(\bar{E}) \cdot P(E)} \\ \\& =\frac{3}{4} \cdot \frac{3}{4} \cdot \frac{1}{4}=\frac{9}{64} . \end{aligned}

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seema garhwal

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