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Question
Solve the following problem :
If a fair coin is tossed 4 times, find the probability that it shows 3 heads
Solution
Let X denote the number of heads.
P(getting head) = p = `(1)/(2)`
∴ q = 1 – p = `1 - (1)/(2) = (1)/(2)`
Given, n = 4
∴ X ∼ B`(4, 1/2)`
The p.m.f of X is given by
P(X = x) = `""^4"C"_x (1/2)^x (1/2)^(4 - x), x` = 0, 1,....,4
P(getting 3 heads) = P(X = 3) = `""^4"C"_3 (1/2)^3 (1/2)`
= `(4)/(2^4)`
= `(1)/(4)`.
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