Question

Ben has 3 pennies, 1 dime, and one quarter. What is the probability that he can match the change of a dollar bill for any purchase?

Answer 1

To solve this question:
1. Calculate the number of unique values of change that will result by taking the coins 1 at a time, 2 at a time, 3 at a time, 4 at a time and all together. For example if the coins are taken all together a value of 38 cents results, which is 1 unique combination because 38 cents cannot be achieved by any other combination.
Call the total number of unique combinations n.
2. The possible change ranges from 1 cent up to 99 cents giving 99 possible values.
3. The required probability is found from
\[P(match\ $\ bill\ with\ change)=\frac{n}{99}\]