Originally posted by Sweet04Angel
When am I going to win the lottery? I continue to donate dollars, but I have yet to win.
Hopeful in Atlanta
Hello Hopeful in Atlanta:
Thank you for your question.
Winning the lottery is all about odds. You will likely win the lottery one day, but the prize may be only 5 dollars. As for going the big bucks consider this:
Is it better to play 50 dollars one week, or one dollar for fifty weeks?
The odds of a "Lotto" style lottery can be found with the formula: n! / (n - r)! r! where n is the highest numbered ball and r is the number of balls chosen. This is called in math a combination. An easier way to think about it is if there are 40 balls and 6 are chosen, there are 40 possible numbers that can come up first, leaving 39 that can come up second, then 38, 37, 36, and finally 35 on the final number. To find out how many numbers that is you multiply 40 Ã—39 Ã—38 Ã—37 Ã—36 Ã— 35 = 2,763,633,600 making the odds 2 and a half billion to one.
Pretty slim odds, but luckily the order of the balls does not matter, so we can divide this number by how many ways these numbers can be arranged. There are six possibilities for the first ball, five for the second, 4 for the third, 3, 2, and one left over. That is 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 720 So, the odds are 2,763,633,600 Ã· 720 = 3,838,380 to one.
If I put $50 on one lottery, the odds of winning are 3,838,380 Ã· 50 = 76767.6 to one. That is the easy part.
The hard part is calculating the odds of winning if I put $1 on 50 lotteries. To do this we have to convert to probabilities. A probability is a number between 1 and 0. 1 means a perfect chance, 0 means no chance at all. The probability of winning the lottery with one dollar is 1 Ã· 3,838,380 = 0.0000002605... in other words, very small. The probability of winning the lottery with 50 dollars is 1 Ã· 76767.6 = 0.0000130263288...
Just for your information, the probability of winning twice in a row is this number squared which is 0.00000000000006. This is not very useful information except that we can use this formula in reverse to get what we want. The cool thing about probabilities, as opposed to odds, is that the probability of winning is one minus the probability of losing. This leads us to a way of calculating what we want by using a double negative. The probability of winning at least once in 50 tries is the same as the probability of not losing 50 times in a row.
The probability of losing is 1 - 0.0000002605... = 0.9999997394...
The probability of losing 50 times in a row is 0.9999997394... to the 50th power = 0.99998697...
The probability of not losing 50 times in a row is 1 - 0.99998697... = 0.0000130262457...
So, since the probability of winning at least once in 50 tries is 0.0000130262457... and the probability of winning one lottery with 50 dollars is 0.0000130263288... The odds are very very slightly more favorable by playing all 50 dollars in one lottery than spreading it out among 50 lotteries.