What is the probability distribution?

Question

A jar contains 13 coins: 7 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X.

Please enter the values for x in increasing order. Please enter the values for P(X=x) as a number rounded to four decimal places.

__x__ __2__ ____ ____ ____ ____ ____

P(X=x) ____ ____ 0.0128 ____ ____ ____

If you were to randomly draw 2 coins ffrom this jar, how many cents do you expect to have on average? (Round to TWO(2) decimal places)

Answer 1

combination value probability

Penny, Nickel 6 C(7,1) C(2,1)/C(13,2) 14/78 0.18

Penny, Dime 11 C(7,1) C(4,1)/C(13,2) 28/78 0.36

Nickel, Dime 15 C(2,1) C(4,1)/C(13,2) 8/78 0.1

Penny, Penny 2 7/13 * 1/2 21/78 0.27

Nickel, Nickel 10 2/13 * 1/12 3/156 0.02

Dime, Dime 20 4/13 * 1/4 4/52 0.08

E(x) = sum (value * probability) = 6*0.18 + 11 * 0.36 + 15 * 0.1 + 2 * 0.27 + 10 * 0.02 + 20 * 0.08 = 8.88