Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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.

Answer 6

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