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