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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?

 Dec 2, 2019
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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.
(680+408)*9=9792

so, there are 11400-9792 = 1608 winning tickets

1608/11400 = 67/475 

 Dec 2, 2019

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