# A fair coin is tossed 8 times. Find the probability that it shows heads at least once - Mathematics and Statistics

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

#### Solution

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

Concept: Conditional Probability
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