A jar contains 6 pennies, 5 nickels and 6 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Find the probability X = 10. Find the probability X = 11. Find the expected value of X.

Given Information:

No. of Pennies = 6

No. of Nickels = 5

No. of Dimes = 6

Replacement not allowed

X represents amount in cents

Required Information:

a) P (X = 10) = ?

b) P (X = 11) = ?

c) E (X) = ?

Answer:

a) P (X = 10) = 0.073

b) P (X = 11) = 0.264

c) E (X) = 10.70

Step-by-step explanation:

1 penny is equal to 1 cent

1 nickel is equal to 5 cents

1 dime is equal to 10 cents

Total coins = 6P + 5N + 6D = 17

a) Find the probability X = 10

P (X = 10) means selecting 2 nickels so that X = 5 + 5 = 10

P (X = 10) = P (selecting 2 nickels) = 5/17*4/16 = 5/68

P (X = 10) = 0.073

b) Find the probability X = 11

P (X = 11) means selecting 1 penny and 1 dime so that X = 1 + 10 = 11

P (X = 11) = P (selecting a penny and dime) = 2 * (6/17*6/16) = 9/34

P (X = 11) = 0.264

c) Find the expected value of X

We want to select 2 coins from total 17 coins

6 pennies = 6*1 = 6 cents

5 nickels = 5*5 = 25 cents

6 dimes = 6*10 = 60 cents

E (X) = 2 * (6 + 25 + 60) / (6 + 5 + 6)

E (X) = 2 * (91/17)

E (X) = 10.70

Therefore, the expected value of X is 10.70