Answer to Question #219939 in Statistics and Probability for Bless

Question #219939

A box contains five black and five yellow balls. Two balls are withdrawn
randomly.If they are of the same colour, then you win $1.10; if they are of
different colours, then you lose $1.00.Calculate
i. the expected value of the amount you win
ii. the variance of the amount you win.

Expert's answer

"P(same\\; colors)=\\frac{5}{10}*\\frac{4}{9}*2=\\frac{4}{9}."

"P(different\\;colors)=\\frac{5}{10}*\\frac{5}{9}*2=\\frac{5}{9}."

i. "E(X)=\\frac{4}{9}*1.10-\\frac{5}{9}*1.00=-\\frac{1}{15}\\approx0.0667."

ii. "\\sigma^2=\\frac{4}{9}*1.10^2+\\frac{5}{9}*1.00^2-(-\\frac{1}{15})^2=\\frac{82}{75}-\\frac{1}{225}=\\frac{49}{45}\\approx1.0889."