Question

Evaluate C_n.xP^xQn-x For the given n=7, x=2, p=1/2

Answer 1

The value of given expression is
`(21)/(128)`.

Explanation:

Given information: n=7, x=2, p=1/2

`q=1-p=1-(1)/(2)=(1)/(2)`

The given expression is

`C(n,x)p^xq^(n-x)`

It can be written as

`^nC_xp^xq^(n-x)`

Substitute n=7, x=2, p=1/2 and q=1/2 in the above formula.

`^7C_2((1)/(2))^2((1)/(2))^(7-2)`

`(7!)/(2!(7-2)!)((1)/(2))^2((1)/(2))^(5)`

`(7!)/(2!5!)((1)/(2))^(2+5)`

`(7* 6* 5!)/(2* 5!)((1)/(2))^(2+5)`

`21((1)/(2))^(7)`

`(21)/(128)`

Therefore the value of given expression is
`(21)/(128)`.