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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?

 

Hint: Consider complementary counting.

 Aug 15, 2020
 #1
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The probability is C(7,3)*3*C(11,2)/(10*1200) = 77/160.

 Aug 15, 2020
 #2
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Since you have first to match 3 white balls, the chances picking the first matching ball =3/10 * your chances of picking the 2nd ball, 2/9 * your chances of picking the 3rd ball, 1 / 8=3/10 * 2/9 * 1/8 =6 / 720 - This is the probability of matching 3 white balls.

 

To match the red ball, you have 1/10 chance: So, the overall probability of winning the Super Prize would be:

6 /720 * 1/10= 6 / 7200 =1 / 1200

 Aug 15, 2020

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