Law of Random Numbers
Date: 12/22/97 at 17:47:25 From: Scott Christie Subject: Law of random numbers My question is about the law of random numbers. I've recently been debating over the lottery. In Texas we choose 6 numbers between 1 and 50, so the probability of winning is 1/50x49x48x47x46x45. If I were to list every combination of numbers they would all be equally likely to be drawn. So, for example, the combination 1, 2, 3, 4, 5, 6 should be the same probability as say 5, 10, 18, 33, 45, 50. It has been brought to my attention that the law of random numbers changes the odds of picking numbers in order, or close in order. I have been told that numbers in order, such as 1,2,3,4,5,6, have a smaller probability than numbers that are more random. Is this true and how is it proven?
Date: 12/22/97 at 19:48:42 From: Doctor Tom Subject: Re: Law of random numbers Hi Scott, First off, your probability isn't quite right. The number of combinations of 6 things from a set of 50 is: (50*49*48*47*46*45)/(6*5*4*3*2*1) You have to divide by 6! (6 factorial) since the order isn't important. But every combination of numbers is EXACTLY equally likely (assuming that the lottery isn't rigged). So you have exactly the same chance of winning if you pick 1,2,3,4,5,6 or 5,10,18,33,45,50. Think about it this way - if the balls were renumbered, the probabilities should be the same, right? In real lotteries, there may be a good reason not to pick things like 1,2,3,4,5,6, however. I don't know about Texas, but in California, if there are multiple winners, they split the prize. You'd like to avoid that, so what you'd like to do is pick numbers that other folks are unlikely to pick. So for that reason, I'd avoid things that I know superstitious people would tend to use - 7, 13, and probably all the numbers less than 31, since people tend to go for birthdates, etc. If everyone picks numbers totally at random, or if you are the only person playing, any combination is exactly equally likely to win. But one word of advice: "Don't play the lottery." Again, I don't know the rules in Texas, but if you win the California lottery, you're paid in 20 equal yearly installments. So, for example, if you won a million dollars, you'd get $50,000 each year for 20 years. But money in the future is worth less than money today, and with reasonable estimates of interest rates, the 20-year payoff approximately cuts the current value in half. Also, since when you hit the big one you'll be rich, you'll find yourself in the top tax category - currently 39% federal, and whatever it is in Texas (in California, it's about 11%). So in California, that cuts your winnings in half again, so your real prize is only worth about 1/4 of what it appears to be. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.