Question on Lottery Probabilities

AI Thread Summary
Buying 10 tickets in a lottery with odds of 30,000,000 to 1 does not equate to a probability of 1 in 3,000,000. While the odds and probabilities are related, they are not the same, and the calculation involves a specific formula. The joint probability term, which accounts for overlapping chances, is negligible in this scenario. Therefore, while the approximation is close, the exact probability of winning with 10 tickets is slightly different. Understanding the distinction between odds and probabilities is crucial in lottery calculations.
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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