In the SmallState Lottery, three white balls are drawn (at random) from twenty balls numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten balls numbered 21 through 30. When you buy a ticket, you select three numbers from 1-20 and one number from 21-30. To win a prize, the numbers on your ticket must match at least two of the white balls or must match the SuperBall.
If you buy a ticket, what is your probability of winning a prize?
I get 67/475
You miss all 3 white balls, you get three of the 17 numbers that are wrong, so C(17,3) = 680
You hit 1 white ball and miss the others if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 17 white numbers that were not drawn, so 3(17,2)=408
You miss the SuperBall if you have one of the 9 blue numbers that were not drawn.
so, there are 11400-9792 = 1608 winning tickets
1608/11400 = 67/475