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`