In the Powerball drawing, the numbers are selected from two containers. Five white balls from 69 balls numbered 1 through 69 and one from 26 balls (1-26). To win the Powerball jackpot, the person must watch all six balls. What is the probability of winning the jackpot if you buy a Powerball ticket?
The probability of winning the jackpot = the probability of winning five numbers from the first pot x the probability of winning the number from the second pot. And the good news is, the order doesn’t matter. So you have one way of getting out of the so many ways of drawing five white balls. And since the order doesn’t matter, as you know, it is a combination problem.
So you have one chance out of 69C5 ways of getting five white balls AND 26 ways of getting the red ball. Or 1/(69C5 x 26) = 1/292201338. In case you forgot, the formula for combination, s balls from n possibilities,
The number of combinations of n things, taken s at a time = [n!/s!(n-s)!]
Finally, is it worth spending $2 for a ticket that offers a jackpot of $20 million? We’ll see next.
