Question

A fair coin is tossed 8 times. Find the probability that it shows heads at least once

Answer 1

Let X denote the number of heads

P(getting head) = `1/2`, q = 1 − p = `1 - 1/2 = 1/2`

Given, n = 8

∴ `"X" ∼ "B"(8, 1/2)`

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

P(X = x) = `""^8"C"_x (1/2)^x (1/2)^(8 - x), x = 0, 1, 2, ..., 8`

P(at least one head) = P(X ≥ 1)

= 1 − P(no head)

= 1 − P(X < 1)

= 1 − P(X = 0)

= `1 - ""^8"C"_0 (1/2)^0 (1/2)^8`

= `1 - (1)(1) xx 1/256`

= `255/256`