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!
:)
