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.

Answer 1

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`