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PART 1

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 the three white balls AND the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?

 

 

PART 2

 

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?

 Jun 17, 2021
edited by Guest  Jun 17, 2021
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(1) The probability is 1/C(20,3) = 1/1140.

 

(2)

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.

 Jun 17, 2021

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