perplexus.info :: Probability : Playing Lotto

Playing Lotto (Posted on 2005-01-14)

A Lotto bet is picking 6 numbers out of 49 -- if you pick the correct combination, you get the jackpot!

If N persons play, there will be many repeats, since it's highly probable that some combinations will be chosen by two persons or more. (This is known as the "birthday paradox".)

What's the expected number of DIFFERENT combinations that will be chosen, if N persons play? (Assume these persons pick their combinations totally randomly.)

Submitted by Federico Kereki

Rating: 4.0000 (4 votes)

Solution: (Hide)

If there are C possible distinct combinations, the odds of nobody winning are (1-1/C)^N, so the odds of somebody winning are 1-(1-1/C)^N, which represents the percentage of played distinct combinations, so the answer is C(1-(1-1/C)^N).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2023-09-30 09:20:43
re(2): A simpler way of getting to solution	Steve Herman	2005-01-18 17:17:10
re: A simpler way of getting to solution	Jay Schamel	2005-01-18 11:32:06
re(2): Stirling Perhaps	owl	2005-01-16 21:06:36
A simpler way of getting to solution	Steve Herman	2005-01-16 12:02:45
re(3): my solution....QUESTION	Jay Schamel	2005-01-15 21:34:56
re(2): my solution....QUESTION	Ady TZIDON	2005-01-15 21:04:24
re: Stirling Perhaps	Charlie	2005-01-15 16:33:57
re: my solution	Charlie	2005-01-15 15:45:14
my solution	Ady TZIDON	2005-01-15 07:40:44
re: Stirling Perhaps	Charlie	2005-01-15 04:58:53
Stirling Perhaps	owl	2005-01-14 22:43:47
solution	Charlie	2005-01-14 19:35:20
thoughts	Charlie	2005-01-14 19:00:49

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