Probability of Picking Coins

Date: 01/12/2003 at 12:31:51
From: Kita
Subject: Probability

Max has 5 coins in his pocket that total 47 cents. What is the 
probability that he will reach into his pocket and pull out a dime, 
and then without replacing it reach in and pull out a quarter?

  A. 1/20
  B. 1/10
  C. 1/25
  D. 2/25

Could it be 1/10?

Date: 01/12/2003 at 22:02:38
From: Doctor Kastner
Subject: Re: Probability

Hi Kita -

Not only could it be 1/10, it is 1/10. But why?

Let's first think about the coins that Max has in his pocket. 5 coins,
47 cents. He has to have 2 pennies in order to make the 47, so that
takes care of two of the coins. Now we need to think how he could have
3 coins that make 45 cents. How could he get the 5 cents of the 45?
If he had a nickel, that would mean we need to get two coins to make
40 cents and that can't happen. Therefore, he has to have a quarter,
which leaves us with making 20 cents with two coins. That gives him
two dimes.

So in Max's pocket he has 2 pennies, 2 dimes, and 1 quarter.

Now we can finish the problem off. He has two chances of pulling out a
dime from his five coins, and then he has 1 chance of pulling out a
quarter from the coins he has left. Remember that these probabilities
need to be multiplied together and you'll not only get your answer but
will be able to explain how you got there.

I hope this helps.  Write back if you're still stuck, or if you have
other questions.

- Doctor Kastner, The Math Forum
  http://mathforum.org/dr.math/