Question

An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.

Answer 1

Let p = success,

q = failure

Here n = 5

Given p = 3q

∴ p = 3(1 – p)

∴ 4p = 3,

∴ p = `3/4`

∴ q = 1 – p = `1 - 3/4 = 1/4`

Here X = Number of success

Then X ∼ B(n, p),

n = 5,

p = `3/4`,

q = `1/4`

∴ P(x) = ⁿC_x p^x · q^n–x

= `""^5C_x(3/4)^x(1/4)^(5-x)`

∴ P(x = 2) = `""^5C_2(3/4)^2(1/4)^3`

= `5.4/2*9/16*1/64`

= `90/(16 xx 64)`

= `45/(8 xx 64)`

= `45/512`