MHB Probability of same results for 2 pools

[FrankP]

The question is “What is the probability of one person buying a single ticket for two different football pools and ending up with the same numbers”?

The football pool used is a 10 by 10 array with the numbers 0 through 9 randomly assigned along the x and y axis. One axis is team A, the other team B. There are 100 cells to be purchased individually and assigned randomly. You win if, at the end of a quarter, the last digit of the scores correspond to your purchased cell(s). Example: if you are assigned the cell corresponding to 3 for team A and 7 for team B, you will win if, at the end of a quarter, the score is team A is 23 and team B is 17.

You purchase one cell for one pool and one cell for a separate pool and are randomly assigned the same exact results (team A 7 and team B 3) for each even though the axis numbers were random and different for both and the cell randomly assigned was different for both.

What are the chances of this happening?

I'm thinking the possible number of ways these two pools can be created is 100! squared but that's as far as I can get.

 

[Jameson]

The question is “What is the probability of one person buying a single ticket for two different football pools and ending up with the same numbers”?

The football pool used is a 10 by 10 array with the numbers 0 through 9 randomly assigned along the x and y axis. One axis is team A, the other team B. There are 100 cells to be purchased individually and assigned randomly. You win if, at the end of a quarter, the last digit of the scores correspond to your purchased cell(s). Example: if you are assigned the cell corresponding to 3 for team A and 7 for team B, you will win if, at the end of a quarter, the score is team A is 23 and team B is 17.

You purchase one cell for one pool and one cell for a separate pool and are randomly assigned the same exact results (team A 7 and team B 3) for each even though the axis numbers were random and different for both and the cell randomly assigned was different for both.

What are the chances of this happening?

I'm thinking the possible number of ways these two pools can be created is 100! squared but that's as far as I can get.

Hi FrankP,

Hmm, I might be missing something about the problem but this could be a lot simpler than it seems. So each card is a 10x10 grid with 100 distinct values. You get 1/100 on one card and 1/100 on the other. So assuming you know you have 1 value, the chance of getting the matching value on the other card is 1/100.

This is if the cards have the exact same values of course, but as I understand it that is true. The layout doesn't matter if it's completely random. The last digit of the score also doesn't matter since the grid is pre-defined as 0-9 and A,B.

Am I missing something about the question? Sometimes we like to do analysis on the last digit of a number and how probability works with that, but I don't see that here.