Question

A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of at least 3 successes

Answer 1

Let X denote the number of odd numbers.

P(getting and odd number) = p = `(3)/(6) = (1)/(2)`

∴ q = 1 – p = `1 - (1)/(2) = (1)/(2)`

Given, n = 4

∴ X ∼ B`(4, 1/2)`

The p.m.f. of X is given by

P(X = x) = `""^4"C"_x(1/2)^x(1/2)^(4 - x)`

= `""^4"C"_x(1/2)^4 , x` = 0, 1,...,4

P(at least 3 successes)

= P(X ≥ 3)

= 1 – P(X < 3)

= 1 – P(X = 0 or X = 1 or X = 2)

= 1 – [P(X = 0) + P(X = 1) + P(X = 2)]

= `1 - [""^4"C"_0(1/2)^4 + ""^4"C"_1(1/2)(1/2)^3 + ""^4"C"_2 (1/2)^2(1/2)^2]`

= `1 - [1/16 + 4/16 + 6/16]`

= `1 - (11)/(16)`

= `(5)/(16)`

= 0.3125