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Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals

A

`(25)/(169)`

B

`(52)/(169)`

C

`(49)/(169)`

D

`(24)/(169)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let p=probability of getting an ace in a draw=probability of success
and q=probability of not getting an ace in a draw= probability of failure
Then, `p=(4)/(52)=(1)/(13)`
and `q=1-p=1-(1)/(13)=(12)/(13)` ltbrlt Here, number of trials, n=2
Clearly, X follows binomial distribution with parameter
`n=2 " and "p=(1)/(13)`. Now, `P(X=x)=overset(2)""C_(x)((1)/(13))^(x)((12)/(13))^(2-x) ,x=0,1,2`
`:. P(x=1)+P(X=2)`
`=overset(2)""C_(1)((1)/(13))^(1)((12)/(13))+overset(2)""C_(2)((1)/(13))^(2)((12)/(13))^(0)`
`=2((12)/(169))+(1)/(169)`
`=(24)/(169)+(1)/(169)=(25)/(169)`
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