Question

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

Answer 1

Bernoulli trials are made up of repeated coin tosses.

Let X denote the number of heads obtained in an 8 trial experiment.

∴ X ∼ B(n, P) with n = 8,

p = `1/2`,

q = `1 - p = 1 - 1/2 = 1/2`

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

= `""^8C_x(1/2)^x(1/2)^(8 - x)`

At most once:

P(X = 0) + P(X = 1)

= `""^8C_0(1/2)^0(1/2)^8 + ""^8C_1(1/2)^1(1/2)^7`

= `(1)(1)*(1/2)^8 + 8(1/2)^8`

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

= `1/256 xx 9`

= `9/256`