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Question
A Fair coin is tossed 5 times, find the probability that coin shows exactly three times head
Solution
Let X denote the number of heads.
P(getting head) = p = `1/2`
∴ q = 1 – p
= `1 - 1/2`
= `1/2`
Given, n = 5
∴ `"X" ∼ "B"(5, 1/2)`
The p.m.f. of X is given by
P(X = x) = `""^5"C"_x(1/2)^x (1/2)^(5 - x)`
x = 0, 1, 2, ..., 5
P(exactly three heads) = P(X = 3)
= `""^5"C"_3(1/2)^3 (1/2)^2`
= `10/2^5`
= `5/16`
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