A jar contains 8 pennies, 3 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.

Find the expected value of X.

0,0987

0.02

To find the expected value of X, we need to calculate the sum of all possible outcomes multiplied by their respective probabilities.

First, let's calculate the probability of each outcome. The total number of coins in the jar is 8 + 3 + 4 = 15.

The probability of selecting a penny on the first draw is 8/15, since there are 8 pennies out of 15 coins in total.

After removing one coin from the jar, there are 14 coins left. If a penny was selected on the first draw, there are 7 pennies left out of the remaining 14 coins. Therefore, the probability of selecting a penny on the second draw given a penny was selected on the first draw is 7/14.

Following the same reasoning, we can calculate the probabilities for nickels and dimes:

- Probability of selecting a nickel on the first draw: 3/15
- Probability of selecting a nickel on the second draw given a nickel was selected on the first draw: 2/14

- Probability of selecting a dime on the first draw: 4/15
- Probability of selecting a dime on the second draw given a dime was selected on the first draw: 3/14

Now, we can calculate the sum of all possible outcomes multiplied by their probabilities.

For pennies:
(1 cent + 1 cent) * (8/15) * (7/14) = 56/105 cents

For nickels:
(5 cents + 5 cents) * (3/15) * (2/14) = 6/105 cents

For dimes:
(10 cents + 10 cents) * (4/15) * (3/14) = 12/105 cents

Adding up all the outcomes:
(56/105) + (6/105) + (12/105) = 74/105 cents

Therefore, the expected value of X is 74/105 cents, or approximately 0.7047 cents.