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?
+23246 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:
3C2·7C1 / 10C3 = 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:
3C3·7C0 / 10C3 = 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.
