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In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from 1 to 12, and one SuperBall is drawn (at random) from red balls numbered from 13 to 20. When you buy a ticket, you choose three numbers from 1 to 12, and one number from 13 to 20.

 

If the numbers on your ticket match two of the three white balls or 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?

 Jan 15, 2023
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1 - [(3/12) (2/11) (1/10)] = 1 / 220

 

2 - [+ 3 (3/12) (2/11) (9/10)] = 27 / 220

 

3 - [+ (1/8 - (1/8) (3/12) (2/11) (1/10))] = 219 / 1760

 

4 - [- (1/8) 3 (3/12) (2/11) (9/10)] = - 27 / 1760

 

5 - The probability is: [1 / 220  +  27 / 220  +  219 / 1760]  -  27 / 1760 = 13 / 55

 Jan 15, 2023

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