What is the probability of drawing the same numbers in a lottery multiple times?

[erotavlas]

This is a question relating to lotteries. Bascially everyone says that each draw is totally independent of each other. So the probability of generating a sequence of numbers each time is the same no matter what the numbers are. However for two draws, there must be a way to calculate the probability that the same set of numbers would be drawn a second, third, fourth... time. This event would be extremely unlikely yet still could occur.
Is ther a value we can give to these unlikely occurences?

 

[mathman]

Let P be the probability that a set is drawn. Then the probability that, if a set is drawn, it is repeated on the next draw is P. On the next two draws it is P², etc.

 

[erotavlas]

Thanks
So then why is it each draw is considered independent of each other, if say the next draw probability P is independent on not having the exact same numbers as the previous draw (since otherwise it would be P²

 

[mathman]

Thanks
So then why is it each draw is considered independent of each other, if say the next draw probability P is independent on not having the exact same numbers as the previous draw (since otherwise it would be P²

Please clarify your question.

 

[erotavlas]

I guess I'm referring to dependent vs dependent events. If it is claimed that lottery draws are dependent of each other (i.e. one draw has no influence on the outcome of the next draw) However doesn't this contradict with the change in probability for two consecutive draws where the event is identical?

Say I play the same lottery numbers every week. The probability that they draw my numbers is P. I continue to play my numbers the following week but the probability that they draw my numbers on the next draw doesn't remain P, doesn't it change to P² as was stated in the previous response? If so wouldn't that mean there is some dependence on the previous draw (because the probability changed)?

 

[Number Nine]

...doesn't it change to P² as was stated in the previous response?

I don't see where he said that anywhere. He said that the probability of a specific sequence being repeated on the next two trials is P², which is true.

 

[Antiphon]

The odds of drawing number x is p. The odds of drawing it twice is P squared but only if this is specified in advance.

If you draw x then the probability of drawing x the second time is p.

 

[erotavlas]

I don't see where he said that anywhere. He said that the probability of a specific sequence being repeated on the next two trials is P², which is true.

Is this correct?

1st attempt => draw numbers N = probability P
2nd attempt => draw same numbers N = probability P
3rd attempt => draw same numbers N = probabiloty P²
4th attempt => draw same numbers N = probability ?

The odds of drawing number x is p. The odds of drawing it twice is P squared but only if this is specified in advance..

What does this mean, specified in advance?

 

[Number Nine]

Is this correct?

1st attempt => draw numbers N = probability P
2nd attempt => draw same numbers N = probability P
3rd attempt => draw same numbers N = probabiloty P2
4th attempt => draw same numbers N = probability ?

No. The probability is P at every step.

 

[erotavlas]

No. The probability is P at every step.

So then what was P²?
I'm really confused now.

 

[Zula110100100]

anytime you draw, the probability of getting x is P, but the probability of getting x twice is P² This -requires- looking at two draws, not just one. P is for one draw, anyone draw, but not TWO draws. methinks. Perhaps it is three...I would have thought two. Clarification there? But certainly more than one! And that is what changes the probability, the number of draws you are looking at

 

[Antiphon]

Let's use coins. The probability of flipping tails is 0.5 every time regardless of the history of the prior flips.

But if you specify in advance that you wish to flip 10 tails in a row, the probability of that entire sequence of flips is 1/2^10, about 1024:1.

Once you have reached the ninth toss and it has come up tails, then the probability of flipping the tenth tail is 0.5 even though your odds of getting to the ninth flip were 512:1.