Originally Posted by nomadicwarrior
I have just had a disagreement with a friend who thinks that your chance of winning the lottery is greater if your buy five tickets in one week than if you were to buy one ticket per week over five consecutive weeks.
What does every think about this?
He's correct, but the difference will be insignificant when the chance of winning is small. When you buy 5 different tickets in 1 week, you have 5 times the probability of winning the grand prize than if you bought 1 ticket. When you buy 1 ticket per week for 5 weeks, your chances of winning will be very slightly less than 5 times the probability for 1 ticket because of the very small chance that you will win more than once. The 5 tickets in the same week represent mutually exclusive outcomes because only 1 can win, while the 5 tickets over 5 weeks represent independent outcomes. Note that the probabilities would be exactly the same if all 5 tickets were chosen randomly since in that case you could possibly get duplicate winning tickets when you play 5 in the same week, and that has the same probability as winning multiple times over 5 different weeks because then the tickets would be independent in both cases.