Probability from Scrabble

Hi, folks,

How would I go about answering the following question:

If there are a total of 10 letter tiles left, 2 of which are the letter "D," and my opponent has 7 letters in his tray, what is the probability that one of those letters is a "D"?

Thanks in advance.

t

tuneguy said:

Hi, folks,

How would I go about answering the following question:

If there are a total of 10 letter tiles left, 2 of which are the letter "D," and my opponent has 7 letters in his tray, what is the probability that one of those letters is a "D"?

Thanks in advance.

t

Click to expand...

A nice intro to combinations and permutations is, IMO,
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Hint: A nice thing to remember in working some probability problems is that the probability of something happening is one minus the probability of something not happening. That is, assuming it is either going to happen or not which is true for most all things. So maybe the way to approach this is to find the probability that your opponent has neither D. We can start be noting that we have 8 choices for the first letter, 7 choices for the second letter, etc. But that implies a particular order so we need to divide by the number of way that set of choices can be rearranged to remove the duplicates [see order matters = permutations and order doesn't matter = combinations in the above link]. After that, what is the number of total choices when you choose 7 things from 10 items and order doesn't matter. The ratio gives the probability and one minus that gets you to where you want.

So you have 3 tiles since your opponent has 7 and there are 10 tiles in total. Now the probability that you opponent has 1 D equals the probability that you have one D (since there are 2 Ds in total). Now the probability that any given tile is a D is 2/10 (read as 2 out of 10!!!!) and the probability of not being a D is 8/10. So you want to find the probability that if you have 3 tiles then you have 1 D (I use the case of 3 tiles instead of 7 only because 3<7) which is equivalent to the probability that if you choose 3 tiles from 10 that you get exactly 1 D.
Read up on binomial distributions.