Wikipedia:Reference desk/Archives/Mathematics/2014 April 13

= April 13 =

Lotto odds for 2 tickets
Hi can you help, If the odds on a lotto ticket are 1 in 14 million does that mean the odds on 2 tickets are 2 in 7 million or 2 in 14 million? Thanks — Preceding unsigned comment added by 92.23.159.60 (talk) 16:43, 13 April 2014 (UTC)


 * 2 in 14 million, or one in 7 million. IBE (talk) 00:26, 14 April 2014 (UTC)


 * Almost exactly. If in the first case there were 14 million tickets sold and you had one, then if you bought a second ticket there would be 14 million and 1 tickets sold, so your average return would go down a bit for the 2nd ticket (in terms of your chances of having to share the pot with yourself if both tickets win).  Think about it this way, buying 14 million tickets wouldn't guarantee you 100% of the pot, because there would still be those other pesky 14 million or so people with tickets. StuRat (talk) 02:34, 14 April 2014 (UTC)


 * There are different kinds of lotteries. In the kind where every ticket has a unique number and only one ticket wins, then buying two tickets doubles your chance of winning (in this case, to 1 in 7 million, as It's Been Emotional says).  In the kind where you pick your own combination of numbers, but only one combination wins and different people with that combination share the prize, if you pick a different combination then the calculation is the same&mdash;again you double your chance of winning.  But in that type of lottery if you buy two tickets with the same combination (yes, this has actually happened), then your chance of winning doesn't change (it's still 1 in 14 million), but you can get a double share of the prize if you aren't the only one who picked that combination.


 * "Sharing the pot with yourself", as in StuRat's answer, is only relevant if you did buy two tickets with the same combination or if there are multiple winning combinations (also possible in some lotteries, especially for secondary prizes, but I assume from the question statement that we're only being asked about the main prize).


 * "Average return" is also irrelevant; the question was about the chance of winning, not the amount. --50.100.193.30 (talk) 03:54, 14 April 2014 (UTC)


 * Yes, I assumed it was one of those where you pick the numbers. In Australia, the lottery is where you just buy a ticket with a number. Lotto is where you pick the numbers.

The winning probability of one ticket is p=1/14000000. The losing probability of one ticket is 1−p. The probability that two tickets both lose is (1−p)2. The probability that two tickets do not both lose is 1−(1−p)2 = 2p−p2 = 27999999/196000000000000 which is less than 1/7000000. Bo Jacoby (talk) 19:04, 16 April 2014 (UTC).


 * This is correct as well, for yet another possible scenario, different from the ones I described above. It is possible in some lotteries to either choose your own combination or have one chosen at random.  Bo's calculation is correct if you don't know whether the two tickets have the same combination of numbers or not, perhaps because at least one of them was chosen at random. --50.100.193.30 (talk)  — Preceding undated comment added 22:03, 16 April 2014 (UTC)