Understanding Probability in Lottery Odds: A Misconception

[mlovas]

My husband and I disagree. A hospital lottery claims the odds are 1 in 3 to win a prize. There are 72,000 prizes and 250,000 tickets.

Assuming a winning ticket is removed from the pot for the next draw, I say the odds or chances of winning are at best 1 in 178,000. If winning tickets go back in for each subsequent draw, I say your odds of winning never exceed 1 in 250,000 notwithstanding that there are 72,000 draws.

My husband says the odds are 1 in 3 (approximately).

Please setlle this dispute. I believe the only way the odds can be 1 in 3 is if the 250,000 tickets are separated into 72,000 groups of three tickets and there is a draw from each of the 72,000 groups of 3 tickets for a prize. I am tired of people not understanding that this is highly misleading telling people they have a 1 in 3 chance of winning a prize. Am I wrong?

Thanks.

Mary

 

[Pengwuino]

If someone can't win a second prize, then there is approximately a 1 in 3 chance of winning (actually, it's 1 in 250,000/72,000 odds). It literally means 1 in every 3 people will win a prize. This is very very likely the way the lottery is held. What "1 in Y chances" means in the most literal sense is that out of every Y number of people, 1 will win. So if you literally think about spreading out 72,000 prizes amongst 250,000 people, you clearly have 1 in 3 odds - that is, 1 out of every 3 people or so will win a prize).

If someone is allowed to win a second prize, the odds become smaller, but nothing crazy like 1 in 172,000 or whatever. I believe it becomes 1 in roughly 4 chance that you'll win at least once.

Think about your logic. What if there were 249,998 prizes and 250,000 entries? Based on your logic, you have 1 in 2 odds. Does it really make sense that the odds of you winning one of those 249,998 prizes are 50/50?

 

[mlovas]

I still don't see how the mathematical probability of your ticket being drawn to win a prize increases over 1 in 250,000 for each separate draw for a prize, each draw being a separate event.

Mary

 

[Pengwuino]

I still don't see how the mathematical probability of your ticket being drawn to win a prize increases over 1 in 250,000 for each separate draw for a prize, each draw being a separate event.

Mary

This is what I figured you were thinking about but wasn't sure. Think of it this way - label each prize as Prize 1, Prize 2, 3, 4... Prize 72,000. The 1 in 250,000 figure that you're thinking about is specifically "What are my odds of winning Prize #X". So assuming people are allowed to win as many times as they want, then you have a 1 in 250,000 odds of winning Prize #20,350. However, it is SPECIFICALLY prize #20,350. It is overwhelmingly unlikely you will win a specific prize. When they say "you have 1 in 3 odds of winning", all that is being said is that you have a 1 in 3 chance of winning A prize, not a specific prize.

 

[HallsofIvy]

Of course, the great majority of those prizes are worth very little.

 

[tamtam402]

mlovas, I think your misconception comes from the classic misconceptions that lead people to do stuff such as betting on reds in a game of roulette when the last 3-4 results were black. Obviously the previous results don't affect the probabilities of the next ball stopping on a black or red color.

This is very badly explained, english isn't my primary language. However it would be correct to state the chances of winning are about 1 in 3 in this case. As someone else said, you were trying to predict your chances of winning a specific prize out of the 72000. Your chances of winning A prize and not one of the specific prizes are much higher, obviously.