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 P r {N = n} = (n – 1) (52 – n) (51 – n)/50 x 49 x 17 x 13 where 2 ≤ n ≤ 50

Question

Jitender Pal · Answer

Hello Student,

Please find the answer to your question

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 ⁴C₁x ⁴⁸C_{n – 2}/⁵²C_{n -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
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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 P r {N = n} = (n – 1) (52 – n) (51 – n)/50 x 49 x 17 x 13 where 2 ≤ n ≤ 50

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 P_r {N = n} = (n – 1) (52 – n) (51 – n)/50 x 49 x 17 x 13 where 2 ≤ n ≤ 50

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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 P r {N = n} = (n – 1) (52 – n) (51 – n)/50 x 49 x 17 x 13 where 2 ≤ n ≤ 50

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

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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 P_r {N = n} = (n – 1) (52 – n) (51 – n)/50 x 49 x 17 x 13 where 2 ≤ n ≤ 50