You reach into a bag of coins and withdraw two coins. what is the probability you withdrew a nickel and then a dime if the bag held 5 pennies, ten nickels, and four dimes?

The bag holds
5 pennies
10 nickels
4 dimes
For a total of 5+10+4 = 19 coins



For the first selection, the probability of a nickel is 10/19 because there are 10 nickels out of 19 total coins.

After that first selection is made, I'm assuming the nickel is NOT put back. In other words, there's no replacement. If this is the case, then we have 19-1 = 18 coins left. There are 4 dimes out of 18 coins giving 4/18 = 2/9 as the probability of getting a dime for the next selection.

Multiply the two fractions: (10/19)*(2/9) = (10*2)/(19*9) = 20/171

So without replacement, the probability of picking a nickel first and then a dime next is the fraction 20/171, which is approximately equal to the decimal value of 0.11696 (rounded to 5 decimal places).