Question

A jar contains 2 pennies, 7 nickels and 3 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 P(x=10)

(b) Find P(x=11)

(c) Find the expected value of X

Answer 1

1 penny= 1 cent

1 nickel = 5 cent

1 dime = 10 cents

a)

P(X=10) = P(both nickel) = 7C2 / 12C2 = 0.3182

b)

P(X=11) = P(1 dime and 1 cent) = 2/12*3/11*2 = 0.0909

c)

outcome		P(X)
2 penny	=2/12*1/11	0.0152
1 penny 1 nickel	=2/12*7/11*2	0.2121
1 penny,1 dime	=2/12*3/11*2	0.0909
2 nickel	=7/12*6/11	0.3182
1 nickel, 1 dime	=7/12*3/11*2	0.3182
2 dime	=3/12*2/11	0.0455

outcome	X	P(X)	X*P(X)
2 penny	2	0.0152	0.030
1 penny 1 nickel	6	0.2121	1.273
1 penny,1 dime	11	0.0909	1.000
2 nickel	10	0.3182	3.182
1 nickel, 1 dime	15	0.3182	4.773
2 dime	20	0.0455	0.909

mean = E[X] = Σx*P(X) =            11.1667
expected value of X = 11.1667