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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?

 Jul 8, 2020
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Case 1: Superball

 

The probability is 1/10, because you choose 1 out of 10.

 

Case 2: 2 whites

 

The probability is 1/C(10,2) = 1/45, because you choose 2 out of 10.

 

Case 3: 3 whites

 

The probability is 1/C(10,3) = 1/120, because you choose 3 out of 10.

 

Adding these, you get 1/10 + 1/45 + 1/120 = 47/360.

 Jul 9, 2020

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