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May 29, 2020

#1
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hi guest!

so the problem is:

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?

i see that it's an aops problem, so I'll only give you some hints.

there are $$\dbinom{10}{3}\cdot 10=1200$$ total possibilities.

since there are many cases to how you could win, its best to use complementary counting in this case. So, to have a losing ticket, you must have at most one correct white ball, and miss the superball.

1. Missing all 3 white balls: this happens if your ticket contains 3 of the 7 white numbers that weren't drawn, so there are $$\dbinom{7}{3}=35$$ possibilities for that situation.

2. If you hit 1 white ball and miss the others: this happens if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 7 white numbers that weren't drawn, so there are $$3\dbinom{7}{2}=63$$ possibilities for that case.

from here, all you have to calculate are the cases with the superball and subtract them from the total since we are complementary counting.​

i think you can do the rest from there!

you got this!

ask me if you need any more help!

:)

May 29, 2020
edited by lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
edited by lokiisnotdead  May 29, 2020
#2
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For the superball, I got:

There is only 10 numbers from 11 - 20. We take 1 out from those.

9 choose 1 = 9.

May 29, 2020
edited by Guest  May 29, 2020
#3
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ok so yea there are 9 cases with the superball. now just multiply 9 with the other 2 cases in my previous post.

#4
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and then subtract that from the total.

#5
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I got 882/1200. Is that right?

63 + 35 = 98

98 * 9 = 882

Guest May 29, 2020
#6
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ok now subtract that from the total since we are complementary counting (I'm assuming you know what that means)

edited by lokiisnotdead  May 29, 2020
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I got 318/1200. Is that right? If it is, THANK YOU SO MUCH FOR HELPING ME!

May 29, 2020
#8
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yep im pretty sure it is!

edited by lokiisnotdead  May 29, 2020
#9
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also remember to simplify!