# Probability of same results for 2 pools

• MHB
• FrankP
In summary, the question asks if there is a chance of getting the same score on two different football pools if you purchase one cell for each. The answer is that there is a 1/100 chance of this happening.
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.

FrankP said:
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.

## 1. What is the probability of obtaining the same results from two different pools?

The probability of obtaining the same results from two different pools depends on various factors such as the size of the pools, the number of samples taken, and the characteristics of the samples. In general, the probability can range from 0 to 1, with 0 indicating no chance of obtaining the same results and 1 indicating a certainty of obtaining the same results.

## 2. How can we calculate the probability of same results for two pools?

To calculate the probability of same results for two pools, we need to know the size of the pools, the number of samples taken from each pool, and the characteristics of the samples. We can then use mathematical formulas such as the binomial distribution or the hypergeometric distribution to calculate the probability. Alternatively, we can also use statistical software or online calculators to determine the probability.

## 3. Is there a difference in the probability of same results for two pools with different sample sizes?

Yes, the probability of obtaining the same results for two pools can vary depending on the sample sizes. Generally, as the sample sizes increase, the probability of obtaining the same results also increases. However, this also depends on the characteristics of the samples and the size of the pools.

## 4. Can the probability of same results for two pools be affected by external factors?

Yes, the probability of obtaining the same results for two pools can be affected by external factors such as the environment, handling of samples, and equipment used. These factors can introduce bias or errors in the sampling process, which can affect the probability of obtaining the same results.

## 5. How can we increase the probability of obtaining the same results for two pools?

To increase the probability of obtaining the same results for two pools, we can increase the sample sizes, ensure proper sampling techniques, and minimize external factors that can introduce bias or errors. Additionally, we can also use statistical methods such as repeated sampling or randomization to improve the chances of obtaining the same results.

Replies
4
Views
1K
Replies
5
Views
4K
Replies
9
Views
3K
Replies
12
Views
1K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
2
Views
929
Replies
3
Views
1K
Replies
1
Views
2K
Replies
2
Views
2K