Question

A Fair coin is tossed 5 times, find the probability that coin shows exactly three times head

Answer 1

Let X denote the number of heads.

P(getting head) = p = `1/2`

∴ q = 1 – p

= `1 - 1/2`

= `1/2`

Given, n = 5

∴ `"X" ∼ "B"(5, 1/2)`

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

P(X = x) = `""^5"C"_x(1/2)^x (1/2)^(5 - x)`

x = 0, 1, 2, ..., 5

P(exactly three heads) = P(X = 3)

= `""^5"C"_3(1/2)^3 (1/2)^2`

= `10/2^5`

= `5/16`