Let the random variable X follow B (6,p). If 16 `P(X = 4) = P(X= 2)`, then what is the value of p?

Options

A. `(1)/(3)`
B. `(1)/(4)`
C. `(1)/(5)`
D. `(1)/(6)`

Answer

C

Explanation

X follows B(6,p) =16P(x = 4) = P(x =2)
`rArr 16 ""^(6)C_(4) . P^(4) (1-p)^(6-4) = ""^(6)C_(2).p^(2)(1-p)^(6-2)`
`rArr 16 xx (6!)/(4!2!)p^(4)(1-p)^(2) = (6!)/(2!4!)p^(2)(1-p)^(4)`
`rArr 16p^(2) = (1-p^(2)) rArr 16p^(2) =1 +P^(2) - 2p`
`rArr15p^(2) = 2p -1 =0 rArr 15p^(2) + 5p - 3p - 1 =0`
`rArr p = (1)/(5),-(1)/(3)`
As `P gt 0 rArr P = (1)/(5)`