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?

3/16 is sadly wrong...

313/2500 is sadly wrong...

141/1000 is sadly wrong...

Guest May 28, 2020

#3**+1 **

I have seen this AoPS question.

10 or so times. Search it with search bar.

hugomimihu May 28, 2020

#5**+2 **

As I said, i have given hints to people asking this question.

No offense, I'm just pretty tired and unwilling to dig up my PDF files, so navigate to the search bar and find this question.

Or.

The probability of reaching at least 2 correct numbers is \(\binom{7}{3}\)

Perhaps this is what you are looking for?

I apologize for the late reply as I was rather busy.

hugomimihu
May 28, 2020

#7**0 **

hi guest!

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

there are \(\dbinom{10}{3}\cdot10=1200\) 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!

:)

lokiisnotdead 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

edited by lokiisnotdead May 29, 2020