+82 In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from $1$ to $12,$ and one SuperBall is drawn (at random) from red balls numbered from $13$ to $20.$ When you buy a ticket, you choose three numbers from $1$ to $12,$ and one number from $13$ 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?
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?
+1612 Problem 2
To win a super prize, we can match at least two of the white balls or match the red SuperBall.
Case 1: Matching at least two of the white balls
There are 4 ways to match 3 white balls, 12 ways to match 2 white balls, and 54 ways to match 1 white ball. Therefore, there are 4+12+54=70 ways to match at least two of the white balls.
Case 2: Matching the red SuperBall
There are 8 ways to match the red SuperBall.
Therefore, there are 70+8=78 ways to win a super prize.
The probability of winning a super prize is 78/(12*11*10*8) = 1/231.
