Odds of a lottery win with 10,000 choices for numbers, players select 100 numbers per ticket

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Fucko

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If there are 10,000 choices for numbers and players select 100 numbers to go on their ticket, what are the odds of a particular ticket winning if 100 numbers are called in the draw?

Thanks for any help, I'm further looking to work out the odds and a prizepool distribution for lower winners like 5 numbers, 10, 20 etc
 
Do you consider the ticket winning only when all 100 drawn numbers match the number on the ticket?
 
blamocur said:
Do you consider the ticket winning only when all 100 drawn numbers match the number on the ticket?
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For the sake of the immediate question I do, but as I said I'd like to work out the odds for lower matches too like 5/100 etc
 
Is this a part of homework? What have you tried? What are you studying?
 
My quick computations tell me that your chance of winning all 100 numbers is about [imath]1.53\times 10^{-242}[/imath], your chance of winning 50 or more numbers is about [imath]2.73\times 10^{-78}[/imath], and to get 10 or more about [imath]5.2\times 10^{-8}[/imath].
 
No I'm designing a lottery lol not studying anything. I want to make it a relatively slim chance of a jackpot so you can have 5 or 10 billion tickets distributed and have a decent chance of a rollover. I feel like with these numbers though it would never have a winner.
 
Fucko said:
No I'm designing a lottery lol not studying anything. I want to make it a relatively slim chance of a jackpot so you can have 5 or 10 billion tickets distributed and have a decent chance of a rollover. I feel like with these numbers though it would never have a winner.
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Suppose you expect to live to be 100 years old. Suppose you plan to buy 1,000,000,000,000 tickets (that's one trillion tickets) every day. (Your parents buy the tickets when you're a kid.) You would have maybe a 1/15 chance of winning once in your entire lifetime.

Who do you think would buy those tickets? :oops:
 
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stapel said:
Suppose you expect to live to be 100 years old. Suppose you plan to buy 1,000,000,000,000 tickets (that's one trillion tickets) every day. (Your parents buy the tickets when you're a kid.) You would have maybe a 1/15 chance of winning once in your entire lifetime.

Who do you think would buy those tickets? :oops:
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super helpful thanks
 
blamocur said:
I agree -- [imath]10^{-242}[/imath] is pretty small :)
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Can you help me fiddle the numbers down so it's plausible that someone will win once in a while if there's say ten billion tickets for every draw? Like if there's 10 numbers and 1000 choices does that start to get somewhat terrestrial?
 
Fucko said:
Can you help me fiddle the numbers down so it's plausible that someone will win once in a while if there's say ten billion tickets for every draw? Like if there's 10 numbers and 1000 choices does that start to get somewhat terrestrial?
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Let's see what you've tried, so we can see where you're getting stuck. Thank you!
 
stapel said:
Let's see what you've tried, so we can see where you're getting stuck. Thank you!
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I'm not working on math homework lol I'm making a website but if you want me to try and fail first before you help then ok I guess...

I'm thinking I'll leave the numbers as they are provided it's not implausible to get wins on the lower end like 1/100 numbers.

I know if you only get one number on your ticket and there was one number drawn you'd have a 10,000/1 chance of a match. Genuinely unsure how to proceed from there. Do I divide that by 100 twice because there's 100 numbers on the ticket and in the draw? That would make it evens odds of getting one match. Idk how to get to the odds of two matches to be honest
 
Fucko said:
I'm not working on math homework lol I'm making a website but if you want me to try and fail first before you help then ok I guess...
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This forum's purpose is to help people to learn math, as opposed to subcontracting on math-related projects. You can try learning combinatorics, especially combinations, or find someone who is interested in working with you on your project.
 
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