Question

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

Answer 1

Let X = Number of heads

p = probability of getting head in one toss

p = `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 as

P(X = x) = `""^nC_xp^xq^(n - x)`

i.e P(x) = `""^8C_x(1/2)^x(1/2)^(8 - x), x = 0, 1, 2, 3,......,8`

P (getting heads at least once)

P[X > = 1] = 1 – P[X = 0]

= 1 – P(0)

= `1-""^8C_0(1/2)^0(1/2)^(8-0)`

= `1 - (1/2)^8`

= `1 - 1/256`

= `255/256`

P[X > = 1] = 0.996