   SEARCH HOME Math Central Quandaries & Queries  Question from munirah, a student: assume the chances of winning the lottery are 1 in 1000.how many times would you have to play to attain 0.5 probability of winning at least once? This is a question that is more easily answered by the pessimists than by the optimists:

Assume the chances of LOSING the lottery are 999 in 1000.
If you play twice, what are the chances of losing both times?
How about if you play three times? four times?
How many times would you have to play to attain less than 0.5 probability of losing every time?

Claude

If the lottery has 1000 tickets and a single prize, then if you buy 500 tickets you have a 50% chance of winning.

If you are buying independent tickets on separate lotteries so that the odds of winning on different tickets are independent, you would need
ln(0.5) / ln(0.999) = 692.800549

tickets. However, you would have a nonzero chance of winning more than once.

If you play until you win for the first time, and average your total number of plays over many tries, the situation is governed (to a good approximation) by the exponential distribution and again the mean is 500.

Good Hunting - and remember the house always wins in the long run!
RD     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.