Flag Algebra> Cards are drawn one by one at random from...
question mark

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

Hrishant Goswami , 11 Years ago
Grade 10
anser 1 Answers
Jitender Pal
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 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
askIITians Faculty
Last Activity: 11 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments