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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
(b) Given, `X~B=(n=5,p=(1)/(3))`
`:' " " p+q=1`
`:. " " (1)/(3)+q=1 rArr q=(2)/(3)`
Now, `" " 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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