PART 1
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 the three white balls AND the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?
PART 2
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?
(1) The probability is 1/C(20,3) = 1/1140.
(2)
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.
