## tomo 2 years ago A matching problem consists of three civil war battles and three years. Sadly, it has been a while since you've taken 19th century American History, and you can't remember the dates of any battles. So you guess, at random, each of the three, picking a different date for each battle. Find the probability distribution for Y , the number of correct matches. confused @phi

1. tomo

I know the following: 3 battles 3 years guess at random each of the 3 different date for each battle find probability distribution for Y = # of correct matches.

2. tomo

I need to find the probability for Y = 0,1,2, and 3

3. tomo

I think that for P(Y=2) it would be [C(3,1)+C(2,1)]/[C(3,1)+C(3,1)]

4. phi

Let's say the battle and correct year are (A,1), (B,2), (C,3) For A B C in that order, list the possible assignment of years. There are 3!= 6 ways ABC 123 3 correct answers 132 1 correct answer 213 1 correct answer 231 0 correct answers 312 0 correct answers 321 1 correct answer so I would say P(0)= 1/3, P(1)= 1/2, P(2)= 0, P(3)= 1/6 Off hand, I don't know how to figure this out using C notation, but ask Zarkon.

5. tomo

thanks @phi, yeah I tried using combinations, however that was not the right way to do it. I understand that P(2) =0, since if you know two are right, then the third one must also be right.

6. phi

When they give small problems, my instinct is to use brute force.