order or arrangement of the numbers doesn't matter) So you have one chance in 13,983,816 of holding the winning ticket. This probability is 0.0000000715 The more tickets you buy, the greater your chance of winning, of course. Suppose you buy 50 tickets (which will cost you $50). Your chances of winning go up ...they're now a whopping 50 out of 13,983,816, for a probability of 0.000003575 (not much of an improvement!) What about the probability of winning anything? Let's work out your chances of matching anything at all! The probability of matching NONE of the six numbers is: 6C0 is the number of ways of choosing the six losers on your ticket, 49C6 is the total number of ways to choose 6 balls Similarly, the probability of matching ONE of the six numbers is: The probability of matching TWO of the six numbers is: This means that 98% of the time, you won't win anything! The first winning ticket is the one where you match THREE numbers. The probability of this occurring (using the method above once again) turns out to be 0.018, or 1.8%, or about 2 out of 100, or about 1 out of 50. This means you must spend about $50 on average, to hope to win the $10. Are you beginning to get the picture? Your chances of winning the big prize are next to nothing, and the chances of winning even $10 are only one in fifty. Yet people win all the time, of course, because millions of tickets are sold every week, and somebody has to win the prizes. It's just not very likely that it will be any one person in particular (ie: you!) By the way, if you play Lotto 649 twice a week, every week, for the next thousand years, your chances of winning the big jackpot are still only about one percent! |