Two coins are taken at

Question

Two coins are taken at random without replacement from a bag containing 9 nickels, 7 dimes and 5 quarters. Let X denote the random variable given by the total value of the two coins. Find E(X), in dollars, to 4 decimal places.

Answer 1

I will tell you how to do this, but you will have to do the arithmetic for yourself!

List the nine possible outcomes.

Attach a probability to each one; remember the probability on the 2 pick is different from that on the first pick. I suggest that you work with only numerators first and divide by 420 at the end.

The 9 outcomes lead to only 6 possible totals. Add the probabilities for each way of getting that total to get the probability for each total.

Now you have the probability distribution for the random variable you need.

Multiply the probability of each total by the value of each total and add the products.

If you have followed my suggestion, divide by 420 and you will have the required expectation.