A jar contains 3 pennies, 8 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. CorrectFind the probability X = 11. IncorrectFind the expected value of X

1) Probability X = 10 is 20.59%.

2) Probability X = 11 is 6.62%.

3) Expected value of X = 12.12

Step-by-step explanation:

We are given;

Amount of pennies in jar = 3

Amount of nickels in jar = 8

Amount of dimes in jar = 6

Total number of coins in the jar = 3 + 8 + 6 = 17 coins

Now, it is well known that;

1 penny = 1 cent

1 nickel = 5 cents

1 dime = 10 cents

A) Probability X = 10 cents

To achieve 10 cents by selecting two coins from the jar means both coins must be nickels.

Thus;

For the first selection, the probability of selecting a nickel would be 8/17.

The probability that the second coin is also a nickel is 7/16.

the probability of this outcome is; 8/17 * 7/16 = 7/34 = 20.59%.

2) Probability X = 11 cents

To achieve 11 cents by selecting two coins from the jar means one coin must be a penny while the other must be a dime.

For the first selection, the probability of selecting a penny is 3/17. The probability of selecting a dime in the second selection is 6/16.

the probability of this outcome is; 3/17 * 6/16 = 9/136 = 6.62%.

3) The expected value of X will be;

E (X) = 2[ (3 * 1) + (8 * 5) + (6 * 10) ] / (3 + 8 + 6)

E (X) = 2 (103) / 17

E (X) = 206/17

E (X) = 12.12