Question

Find the probability of getting two heads and one tail when three coins are tossed.

Answer 1

Let $S$ be the sample space then

$S=\{H,T\},\{H,T\},\{H,T\}$ then the

event $E$ is $\{HHT,HTH,THH\}$

Let $X$ be a random variable denoting the two heads and one tail.

$P(X=2)=$probability of occurrence of $2$ heads and $1$ tail.

$=P\left(HHT\right)+P\left(HTH\right)+P\left(THH\right)$

$=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{2}.\frac{1}{2}=\frac{3}{8}$