probability?

1.
E(X) = n p = 3
V(X) = n p ( 1 - p ) = 2.64

1 - p = 2.64 / 3 = 0.88
p = 1 - 0.88 = 0.12
n = 3 / p = 3 / 0.12 = 25

P( 4 ≦ X < 8 )
= Σ P( X = x ) , from x = 4 to x = 7
= Σ C(25,x) * 0.12^x * 0.88^(25-x) , from x = 4 to x = 7
≒ 0.17904 + 0.10254 + 0.04661 + 0.01725
≒ 0.345 ..... Ans

2.
( the most likely value of x ) = E(X) = 3

P( X = 3 )
= C(25,3) * 0.12^3 * 0.88^(25-3)
≒ 0.239 ..... Ans