What are your odds of winning the lottery/powerball?

I'm going to use Lotto Texas as an example, but I'll also show the calculation for the multi-state Powerball lotto for those interested.

Lotto Texas is straightforward. You choose six numbers in the range 1 to 54, and if all six are drawn, you win the multi-million dollar jackpot.

Your odds of getting the first number correct are 1 in 54 or (1/54) shown mathematically. Simple.

However, after getting the first number correct, you obviously have to get the second number correct as well. The odds are different however, because there are no longer 54 balls to choose from: there are now 53 remaining. So, your odds of getting the next ball correct are slightly better at 1 in 53 or (1/53).

Now, your odds of getting both the first ball and the second ball correct are (1/54)*(1/53) or 1 in 2,862.

Applying this logic to all six balls yields a formula that looks like this:

(1/54)*(1/53)*(1/52)*(1/51)*(1/50)*(1/49) = 1 in 18,595,558,800 (Google Calculator)

So, we can say your odds of winning Lotto Texas are about 1 in 19 billion-- that's Billion with B.

Powerball odds are similar. There are 59 white balls, and a separate set of 39 "powerballs". Five white balls and one powerball is selected. The probability formula is as follows:

(1/59)*(1/58)*(1/57)*(1/56)*(1/55)*(1/39) = 1 in 23,429,886,480 (Google Calculator)

Those aren't very good odds.

Edited 2 years ago

Bummer. I was sure I was going to win this week!