Question

A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times

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 = 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(exactly 5 heads) = P(X = 5)

= `""^8"C"_5 (1/2)^5 * (1/2)^3`

= `(8!)/(5!3!) xx 1/2^8`

= `(8 xx 7 xx 6 xx 5!)/(3 xx 2 xx 1 xx 5!) xx 1/256`

= `(8 xx 7)/256`

= `7/32`