Expert: Abe Mantell - 5/25/2009

Question
Hi Abe. My name's Danielle. My 7th grade class is doing probability and I'm stuck on a homework question. The question is-

Susan walks into an ice cream shop to get a treat. She reaches into her pocket to see how much money she has and realizes that in addition to her two $1 dollar bills, she has a quarter, a dime, a nickel, and a penny. what is the probability that the coins in her pocket will be able to exactly match the change that is needed to pay for her ice cream?

If you could walk me through step by step, it would be greatly appreciated. Thank you for taking the time to help me.

Answer
Hello Danielle,

Hmm, seems like more information would be needed.

Are we to assume that the cost will be $2 plus some amount of change,
so the total will be more than $2 but less than $3?  If so, then we
can do the following...

Since there are 99 possibilities ($2.01 through $2.99), all we need to
do is count how many different amounts we can form with the change in
her pocket, then divide that by 99...OK?

How many different groupings can we make with the 4 different coins?
If we take only 1 coin, then there are 4:
- Q, D, N, or P ==> 25, 10, 5, or 1 cent(s)

If we take 2 coins, then there are 6:
- QD, QN, QP, DN, DP, or NP ==> 35, 30, 26, 15, 11 or 6 cemts

If we take 3 coins, then there are 4:
- QDN, QDP, QNP, or DNP ==> 40, 36, 31, or 16 cents

If we take all 4 of them, then only 1: QDNP ==> 41 cents

So there are a total of 15 different amounts, out of the possible 99.
So the probability is 15/99 = 5/33 or about 0.152 or about 15.2%

I hope this helps.

TTYL, Abe