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 isA. `(9)/(64)`B. `(27)/(64)`C. `(1)/(4)xx(.^(39)C_(2))/(.^(52)C_(2))`D. none of these

A man draws a card from a pack of 52 cards and then replaces it. After

1.	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 isA. `(9)/(64)`B. `(27)/(64)`C. `(1)/(4)xx(.^(39)C_(2))/(.^(52)C_(2))`D. none of these
Answer» Correct Answer - A Let `A_(i)` be the event of drawing a heart card in ith draw. Then, `P(A_(i))=(.^(13)C_(1))/(.^(52)C_(1))=(1)/(4), i=1,2,3` Required probability `=P(overline(A_(1)) cap overline(A_(2)) cap A_(3))` `=P(overline(A_(1)))P(overline(A_(2)))P(A_(3))=(3)/(4)xx(3)/(4)xx(1)/(4)=(9)/(64)`

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