Fun problem:
We have the “word” HOWMEOWCOW.
If we were to arrange the letters at random, what is the probability that we get the 3 O’S before we get
the C?
Let us use our total probability formula.
There are 10 spaces total. Let us examine each of the ten cases (where we position c).
If C is in spot 1, we cannot have our event.
If C is in spot 2, we cannot have our event.
If C is in spot 3, we cannot have our event.
If C is in spot 4, we CAN HAVE OUR EVENT. Now we need to worry about how many ways this is possible.
The first part of this statement is how many ways can we arrange the O’s before the C. The 2
nd
part of
the statement is how many ways can we arrange the remaining 6 letters after already placing the 3 O’s.
Given C is in the forth spot, there are
3
3
ways to arrange the 3 O’s before the C. Next there are
6
3,1,1,1
ways to arrange the other 6 letters.
What about if C is in spot 5?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 MARTIN
 Conditional Probability, Probability, Probability theory, ways

Click to edit the document details