Question

Four coins are tossed.Let A be the random variable representing the number of heads the occur.Find the value of the random variable A

Answer 1

This is a binomial distribution with $n=4,p=\frac{1}{2}.$

$P(A=0)=C_4^0(\frac{1}{2})^0(\frac{1}{2})^4=\frac{1}{16}.$

$P(A=1)=C_4^1(\frac{1}{2})^1(\frac{1}{2})^3=\frac{1}{4}.$

$P(A=2)=C_4^2(\frac{1}{2})^2(\frac{1}{2})^2=\frac{3}{8}.$

$P(A=3)=C_4^3(\frac{1}{2})^3(\frac{1}{2})^1=\frac{1}{4}.$

$P(A=4)=C_4^4(\frac{1}{2})^4(\frac{1}{2})^0=\frac{1}{16}.$