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Question
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
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