Question
Cards are drawn one by one at random from a well shuffled full pack of 52 cards until two aces are obtained for the first time. If N is the number of cards required to be drawn, then PrN=n where 2≤n≤50, is
Answer: Option A
:
A
Here the least number of draws to obtain 2 aces are 2 and the maximum number is 50 thus n can take value from 2 to 50.
Since we have to make n draws for getting two aces, in (n – 1) draws, we get any one of the 4 aces and in the nthdraw we get one ace. Hence the required probability
=4C1×48Cn−252Cn−1×352−(n−1)
=4×(48)!(n−2)!(48−n+2)!×(n−1)!(52−n+1)!(52)!×352−n+1
=(n−1)(52−n)(51−n)50×49×17×3(on simplification).
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:
A
Here the least number of draws to obtain 2 aces are 2 and the maximum number is 50 thus n can take value from 2 to 50.
Since we have to make n draws for getting two aces, in (n – 1) draws, we get any one of the 4 aces and in the nthdraw we get one ace. Hence the required probability
=4C1×48Cn−252Cn−1×352−(n−1)
=4×(48)!(n−2)!(48−n+2)!×(n−1)!(52−n+1)!(52)!×352−n+1
=(n−1)(52−n)(51−n)50×49×17×3(on simplification).
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