- #1

TheMathNoob

- 189

- 4

## Homework Statement

Suppose that all the cards in a deck of n different cards are placed in a row, and that the cards in another similar deck are then shufﬂed and placed in a row on top of the cards in the original deck. It is desired to determine the probability Pn that there will be at least one match between the corresponding cards from the two decks

## Homework Equations

P(AUB)= P(A)+P(B)-P(AnB)

## The Attempt at a Solution

I already posted this problem before, but it was deleted because of the format. People tell me that my logic is wrong and I think that they are right, but I don't know why I am wrong.

This is how I see it

A B C D E...

C B A D E...

we shall determine the probability that at least one pair will match.

Simpler case

A B C D

A

A good way to do it would be to find the prob that no pair matches. In this case there 3 ways how this can happen so it would be 3/4 the prob that no pair matches in this case.

Similarly

A B C D

A B

The number of outcomes in this case would be 3*3

So for n cards it would be (n-1)(n-1)... n times

so the prob would be

1-π(n-1)/n^2

I am still learning how to use the system in this forum. The multiplicative iterator goes from i=1 to n