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# Cards are drawn one by one at random from a well – shuffled full pack of 52 playing cards until 2 aces are obtained to be drawn, first time. If N is the number of cards required to be drawn, then show that Pr {N = n} = (n – 1) (52 – n) (51 – n)/50 x 49 x 17 x 13 where 2 ≤ n ≤ 50

Jitender Pal
7 years ago
Hello Student,
We must have one ace in (n – 1) attempts and one ace in the nth attempt. The probability of drawing one ace in first
(n – 1) attempts is 4C1 x 48Cn – 2/52Cn -1 and other one ace in the nth attempt is, 3C1/[52 – (n – 1)] = 3/53 - n
Hence the required probability,
= 4.48!/(n – 2)! (50 – n)! x (n – 1)! (53 – n)/52! x 3/53 - n
= (n – 1) (52 – n) (51 – n)/50. 49. 17. 13

Thanks
Jitender Pal