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If random variable X~B(n=5,P=(1)/(3)), t...

If random variable `X~B(n=5,P=(1)/(3))`, then `P(2 lt X lt 4) is equal to

A

`(80)/(243)`

B

`(40)/(243)`

C

`(40)/(343)`

D

`(80)/(343)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `X-B(n=5, p=(1)/(3))`
`therefore p+q=1`
`therefore (1)/(3)+q=1`
`Rightarrow q=(2)/(3)`
`therefore p(2 lt X lt 4)=p(X=3)`
`=""^(5)C_(3)((1)/(3))^(3) ((2)/(3))^(2)`
`=10xx(4)/(3^(5))=(40)/(243)`
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