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 May 23, 2020

#1**+1 **

You can win in any of four ways:

1) Getting two of the three winning white balls and the red SuperBall.

Two of the three wining white balls and one out of seven losing white balls:

_{ 3}C_{2}·_{7}C_{1} / _{10}C_{3} = 3·7/120 = 7/40

Combine this with getting the red SuperBall = 1/10 ---> **7/400**

2) Getting two of the three white balls and not getting the red SuperBall:

The 7/40 from above combined with not getting the red SuperBall = 9/10 ---> **63/400**

3) Getting all three of the white balls and the red SuperBall:

Three of three winning white balls and none of the seven losing white balls:

_{3}C_{3}·_{7}C_{0} / _{10}C_{3} = 1·1/120 = 1/120

Combine this with getting the red SuperBall = 1/10 ---> **1/200**

4) Getting all three of the white balls and not getting the SuperBall:

The 1/120 from above combined with not getting the red SuperBall = 9/10 ---> **3/400**

To get the final answer, you must add the individual answers from above.

geno3141 May 23, 2020