Question on Lottery Probabilities

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SUMMARY

The discussion clarifies the relationship between lottery odds and probabilities, specifically addressing a scenario where an individual purchases 10 tickets in a lottery with odds of 30,000,000 to 1. While the initial assumption that the probability of winning becomes 1 in 3,000,000 is close, it is important to note that odds and probabilities are distinct concepts. The formula for calculating odds is defined as p/(1-p), and while joint probability terms exist, they are negligible in this context and can be disregarded.

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This discussion is beneficial for mathematicians, statisticians, lottery enthusiasts, and anyone interested in understanding the intricacies of probability and odds in gambling scenarios.

Millacol88
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I have a question on the chances of winning a lottery: If you buy 10 tickets in a lottery where the odds of you winning are 30,000,000 to 1, is your probability of winning 1 in 3,000,000?
 
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Millacol88 said:
I have a question on the chances of winning a lottery: If you buy 10 tickets in a lottery where the odds of you winning are 30,000,000 to 1, is your probability of winning 1 in 3,000,000?

Yes, pretty close. The odds are not the same as probabilities (p), but with these small odds, it doesn't make much difference. Odds are defined as p/1-p so 10:1 would be p = 0.1/0.9=0.11 In adding independent probabilities there's also a joint probability term that must be subtracted from the sum, but it's negligible in this case and can be ignored.
 
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