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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. T

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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 the first time in the third draw is A. 9 64 B. 27 64 C. 1 4 × .39C2 .52C2 D. none of these Select the correct answer from above options

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Correct Answer - A Let Ai be the event of drawing a heart card in ith draw. Then, P(Ai)= .13C1 .52C1 = 1 4 ,i=1,2,3 Required probability =P( ¯ A1 ∩ ¯ A2 ∩A3) =P( ¯ A1 )P( ¯ A2 )P(A3)= 3 4 × 3 4 × 1 4 = 9 64

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