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?
PS IMPORTANT: PLEASE EXPLAIN HOW YOU GOT TO THE ANSWER/PROCESS!
this problem is everywhere and most of them are wrong so feel free to check out some websites on google
On average, 1 out of 10 times you will draw the AwesomeBall (and this wins all by itself so we don't care what the other balls are) for a winning probability of 0.10.
Now, for the 9 out of ten times that you do not draw the AwesomeBall:
We will have to get a losing blue ball, I'll call that B (and the probability of getting that losing ball is 0.90).
We can win by getting two or more of the white balls. I'll classify a winning white ball (whose probability is 1/10 = 010)
as W and a losing white ball as L (whose probability is 9/10 = 0.90).
So, we can still win if we have this:
B x W x W x W = (0.90) x (0.10) x (0.10) x (0.10) = 0.0009
B x W x W x L = (0.90) x (0.10) x (0.90) x (0.10) = 0.0081
B x W x L x W = ...
B x L x W x W = ...
Since these are independent, add the above 5 results together, to get 47/200.