Answer to Question #299719 in Statistics and Probability for ChillStudent

Question

Supposed three coins are tossed. Let X be the random variable representing the number of heads occur. Construct a table that shows the sample space and values of the random variable X.

Answer 1

This is a binomial distribution with $n=3,p=\frac{1}{2}.$

Sample space: {(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(H,T,T),(T,H,T),(T,T,H),(T,T,T)}.

$P(X=0)=C_3^0(\frac{1}{2})^0(\frac{1}{2})^3=\frac{1}{8}.$

$P(X=1)=C_3^1(\frac{1}{2})^1(\frac{1}{2})^2=\frac{3}{8}.$

$P(X=2)=C_3^2(\frac{1}{2})^2(\frac{1}{2})^1=\frac{3}{8}.$

$P(X=3)=C_3^3(\frac{1}{2})^3(\frac{1}{2})^0=\frac{1}{8}.$