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?
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.
