2. A jar contains 2 pennies, 6 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.

Question

1.      A jar contains 2 pennies, 6 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.

a.      Find the probability X = 11.

b.     Find the expected value of X

Answer 1

P(x = 11) = P(selecting a penny and dime) = C(2,1)*C(4,1)/C(12,2) = 2 * 4 /(12*11/2) =

8/66 = 4/33

E(X) = 2 * (2*1+6*5+4*10)/(2+6+4) = 12