# Actual vs Expected Number of Lottery Winners

• MHB
• fizzypig
In summary, the conversation discusses the odds of winning a lottery jackpot and the expected number of winners based on a sample size of 50 million tickets. The question is whether it is possible to calculate a p value or use other statistical models to determine if the actual number of winners (7) is within normal expected ranges. The solution is to use a one-proportion z-test rather than a t-test due to the nature of the data.
fizzypig
Hi,

My maths problem involves probability relating to lotteries.

The odds of winning a lottery jackpot are 1 in 14 million. Over a period of time 50 million tickets have been bought, so the expected number of jackpot winners would be 3.5. However the actual number of jackpot winners is 7.

Is it possible to calculate a p value to prove that although the actual number of winners is higher than expected, it is still within normal expected ranges? Or are there any other statistical models that would answer the question?

I've seen worked examples for calculating the p value where all the outcomes are listed in excel, before applying the T test formula, however I'm not sure how to go about doing this when there are 50 million outcomes!

Thanks,

Paul

fizzypig said:
Hi,

My maths problem involves probability relating to lotteries.

The odds of winning a lottery jackpot are 1 in 14 million. Over a period of time 50 million tickets have been bought, so the expected number of jackpot winners would be 3.5. However the actual number of jackpot winners is 7.

Is it possible to calculate a p value to prove that although the actual number of winners is higher than expected, it is still within normal expected ranges? Or are there any other statistical models that would answer the question?

I've seen worked examples for calculating the p value where all the outcomes are listed in excel, before applying the T test formula, however I'm not sure how to go about doing this when there are 50 million outcomes!

Thanks,

Paul

Hi Paul, welcome to MHB!

We are talking about a proportion here, in which case we don't do a t-test but a z-test.
See for instance the One-proportion z-test in this wiki article.

## What is the "Actual vs Expected Number of Lottery Winners"?

The "Actual vs Expected Number of Lottery Winners" refers to the comparison between the number of winners in a lottery drawing and the number of winners that would be expected based on statistical probability.

## Why is the "Actual vs Expected Number of Lottery Winners" important?

This comparison is important because it can help determine if a lottery drawing is fair and random. If there is a significant difference between the actual and expected number of winners, it may indicate that the drawing was not truly random.

## What factors can affect the "Actual vs Expected Number of Lottery Winners"?

The main factor that can affect this comparison is the size of the lottery pool. The larger the pool, the closer the actual number of winners will be to the expected number. Other factors such as the number of tickets purchased and the odds of winning can also play a role.

## How can the "Actual vs Expected Number of Lottery Winners" be calculated?

The actual number of winners can be determined by counting the number of winning tickets in a lottery drawing. The expected number of winners can be calculated by multiplying the total number of tickets sold by the odds of winning.

## What should be done if there is a significant difference between the "Actual vs Expected Number of Lottery Winners"?

If there is a significant difference, it is important for the lottery organizers to investigate the drawing process and ensure that it was fair and random. They may also need to make adjustments to the odds or other factors to ensure a more accurate expected number of winners in future drawings.

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