Beware: Math(s) alert!

in reality, all of this has been a total load of old bollocks
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Rorschach
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Re: Beware: Math(s) alert!

Postby Rorschach » 12 May 2021, 10:22

Good Night Dallas, Texas wrote:
Rorschach wrote:
Good Night Dallas, Texas wrote:There are 1000 independent lotteries. Each lottery has 1000 tickets and one drawn ticket wins each lottery.

If you buy a ticket for each lottery - 1000 tickets in total - what is the probability that you win AT LEAST one of the lotteries?



Aargh!
I can't remember how to calculate it. I know it isn't 1,000 in 1,000 but it has to be better than one in a thousand. I'm stuck there at the moment.


Calculate the probability that you don't win any of the 1000 lotteries.


Actually, I've got a bit of a formula for working it out forming in my head. I don't have time to pursue it right now but I'll get back to this later today.
Bugger off.

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Good Night Dallas, Texas
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Re: Beware: Math(s) alert!

Postby Good Night Dallas, Texas » 15 May 2021, 01:20

Probability of not winning a single lottery is (999/1000)

Since each lottery is an independent event the probability of not winning any of the 1000 lotteries is simply the product of not winning one x 1000 of not winning one so
(999/1000)^1000

Now the probability of not winning any plus the probability of winning AT LEAST one lottery must be 1.

So the probability of winning AT LEAST one lottery is (1- (999/1000)^1000)

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Good Night Dallas, Texas
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Re: Beware: Math(s) alert!

Postby Good Night Dallas, Texas » 15 May 2021, 01:43

Part b is what is the probability of winning AT LEAST 3 lotteries. same conditions.

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C
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Re: Beware: Math(s) alert!

Postby C » 15 May 2021, 23:10

Good Night Dallas, Texas wrote:Probability of not winning a single lottery is (999/1000)

Since each lottery is an independent event the probability of not winning any of the 1000 lotteries is simply the product of not winning one x 1000 of not winning one so
(999/1000)^1000

Now the probability of not winning any plus the probability of winning AT LEAST one lottery must be 1.

So the probability of winning AT LEAST one lottery is (1- (999/1000)^1000)


Correct




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Rorschach wrote:it [Tubular Bells] is indeed a very terrible thing. I had a nice Dusty Springfield song buzzing round my head before that bugger displaced it.