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In the SmallState Lottery, three white balls are drawn (at random) from ten balls numbered 1 through 10, and a blue SuperBall is drawn (at random) from ten balls numbered 11 through 20. When you buy a ticket, you select three numbers from 1-10 and one number from 11-20. 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?

 Feb 7, 2020
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There are 9 possible numbers for the first ball, then 8 possible numbers for the second number, then 7 possible numbers.  There are 9 possible outcomes for the SuperBall, so the answer is (1200 - 9*8*7 - 9)/1200 = 687/1200.

 
 Feb 7, 2020

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