The Powerball multi-state lottery is played by picking 5 numbers between 1 and 5

Question

The Powerball multi-state lottery is played by picking 5 numbers between 1 and 59 (the white balls) and an additional bonus number between 1 and 39 (the red Powerball). Twice a week 5 white balls and a red Powerball are drawn from two separate drums revealing the winning numbers. To win at Powerball, your numbers must match the numbers on the winning balls in any of the following nine ways: 5 white balls + red Powerball (Grand Prize) 5 white balls ($200,000) 4 white balls + red Powerball ($10,000) 4 white balls ($100) 3 white balls + red Powerball ($100) 3 white balls ($7) 2 white balls + red Powerball ($7) 1 white ball + red Powerball ($7) No white balls + red Powerball ($7) What is the probability of winning more than $100 in this lottery?

Explanation / Answer

P(winning more than 100) can happen three ways:
4 white balls + red powerball($10000)
5 white balls($200000)
5 white balls + red powerball(Grand Prize)

The number of possible outcomes:
There are nCr = 59C5 = 59!/(5! * (59-5)!) = 5,006,386 ways to pick your five numbers. And there are
39C1 = 39 ways to pick the powerball. Thus there are 5,006,386 * 39 = 195,249,054 total number of ways that the drawing can occur.

P(4 white balls + red powerball) = This requires matching of 4 out of the 5 winning white balls (and one out of the all the losing) and also matching the only red ball = (5C4 * 54C1) * 1C1 = 5*54 = 270
Thus the odds here are 270/195,249,054

P(5 white balls) = This requires matching all 5 winning white balls and not matching the red winning ball
= 5C5 * (1C0 * 38C1) = 1*1*38 = 38
Thus the odds here are 38/195,249,054

P(5 white balls + red powerball) = This requires matching all 5 winning white balls and also matching the red winning ball = 5C5 * 1C1) = 1
Thus the odds here are 1/195,249,054

P(winning more than 100) = (270/195,249,054) + (38/195,249,054) + (1/195,249,054) = 0.000001582594095

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.