In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from 1 to 10, and one SuperBall is drawn (at random) from ten red balls numbered from 11 to 20. When you buy a ticket, you choose three numbers from 1 to 10 and one number from 11 to 20.

If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?

Guest Jun 9, 2021

#1**0 **

Case 1: Superball

The probability is 1/10, because you choose 1 out of 10.

Case 2: 2 whites

The probability is 1/C(10,2) = 1/45, because you choose 2 out of 10.

Case 3: 3 whites

The probability is 1/C(10,3) = 1/120, because you choose 3 out of 10.

Adding these, you get 1/10 + 1/45 + 1/120 = 47/360.

Guest Jun 10, 2021