Ted S.

asked • 04/24/21

What are my odds of winning a single prize raffle if I buy 10 tickets?

I’ve seen a raffle type competition online that I would like to enter but wanted to check a claim that the company are making is correct before I do.


Tickets are limited to 650 entries, number are randomly assigned as is the draw and competitions nearly always sell out so let’s assume that there are definitely 650 entries.


I was always under impression that buying 10 tickets would give me 1/55 chance of winning as 1/55 is just 10/550 simplified. But it has since been suggested that maybe this is incorrect?


I used an online probability calculator which said my assumption is correct but I’ve since spoken to someone who suggested that this is incorrect as the only way to get 1/55 odds is if there is only 55 tickets in the draw and you buy 1 of them.


could you please help?

1 Expert Answer

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William W. answered • 04/24/21

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I'm a little confused at your question because initially you say 650 entries but then you start talking 550. I'll assume there are 650 entries. If you buy 10 tickets and the winner is indeed chose at random, then the PROBABILITY of winning is 10/650 or 1/65. The ODDS of winning is 10/(650 - 10) = 10/640 = 1/64


Notice the probability and odds are different. Probability is the total number of success divided by the total number of possibilities while odds is the total number of successes divided by the total number of failures.

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Ted S.

Hi, thanks for the response. The question was actually based on 550 tickets and not 650. My understanding was that owning 10 tickets would give you a 1/55 chance of winning. But here is the message that I got that made me question this. Could you tell me if there is any merit at all to what is being said below please:..... I assure you the the claim that owning 10 of 550 tickets gives 1 in 55 odds is most definitely incorrect. It's not an opinion. And if you follow the logic through, you will come to the same conclusion... Because buying 10 tickets does not in any way eliminate the chance that any one of the remaining 540 entries could still win! It's as simple as that. If I have 10 tickets, ANY of the other 540 remaining tickets could still win. Each ticket always and immovably represents a 1 in 550 chance (0.1818%) of winning. If I buy 10, I have a 10 chances in 550 (1.818%). So I still only have a 1.818 chance of winning with 10 tickets. If I buy 55 tickets, I still would have a 10% chance of winning, and so on. To actually achieve 1 in 55 odds, one would need to own 495 of the available 550 tickets. Then, and only then, it would mean either me OR one of those 55 remaining active ticket holders could possibly win. I would have effectively reduced the winning ticket pool to either one of my 495 or one of the remaining 55 others. That, and only that, presents a 1 in 55 chance for me only to win. 1 of 550 tickets is 1 in 550 odds. 10 in 550 tickets is therefore 10 in 550 odds, not 1 in 55.
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04/25/21

William W.

If you measure the length of a room, you can measure it using a variety of different units. You could use feet; you could use meters; you could use other units of measure. None of these change the actual length of the room. They are just different units of measure. In your case, you are getting the units of measure confused regarding your chances to win. "Probability" and "Odds" are two DIFFERENT measures of winning. If you measure your chances to win as "probability" you determine your possible number of wins and divide it by the total possible number of tickets. So purchasing 10 tickets from a pool of 550 tickets gives you a probability of 10/550 (which is the same as 1/55). If you measure your chances to win as "odds", you determine your possible number of wins and divide it by your possible number of "looses". So purchasing 10 tickets from a pool of 550 tickets gives you an odds of winning of 10/540 (the same as 1/54). If you purchase 540 tickets, your probability of winning is 540/550 (54/55) while your odds of winning are 540/10 (or 54/1). Neither of these methods of measure change your chance of winning, again, they are just DIFFERENT ways of measuring it.
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04/25/21

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