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Question
Solve the following problem :
If a fair coin is tossed 4 times, find the probability that it shows head in the first 2 tosses and tail in last 2 tosses.
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 head in the first 2 tosses and tail in last 2 tosses.)
= P[X = 2] = `4C_2(1/2)^4`
=`(4xx3)/(2xx1)xx1/16`
= `6 xx 1/16`
= `3/8`
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