Answer to Question #226575 in Statistics and Probability for Carmen

Question

A bag contains four 50 cents and six 20 cents. 2 coins are then out from the bag randomly, find it's expected value.

Answer 1

$P(X=40)=\frac{C_6^2}{C_{10}^2}=\frac{15}{45}=\frac{1}{3}.$

$P(X=70)=\frac{C_4^1C_6^1}{C_{10}^2}=\frac{24}{45}=\frac{8}{15}.$

$P(X=100)=\frac{C_4^2}{C_{10}^2}=\frac{6}{45}=\frac{2}{15}.$

$E(X)=40*\frac{1}{3}+70*\frac{8}{15}+100*\frac{2}{15}=\frac{960}{15}=64$ cents.