1) In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from to , and one SuperBall is drawn (at random) from ten red balls numbered from to . When you buy a ticket, you choose three numbers from to and one number from to .
If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?
2) In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from to , and one SuperBall is drawn (at random) from ten red balls numbered from to . When you buy a ticket, you choose three numbers from to and one number from to .
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 tried this problem multiple times, but all of my attempts were incorrect. Can someone please help?
We compute the complement: we'll count the number of losing tickets.
We saw in part (a) that there are 1200 total possibilities.
To have a losing ticket, you must have at most one correct white ball, and miss the SuperBall.
You miss all 3 white balls if your ticket contains 3 of the 7 white numbers that were not drawn, so there are possibilities.
You hit 1 white ball and miss the others if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 7 white numbers that were not drawn, so there are possibilities.
You miss the SuperBall if you have one of the 9 red numbers that were not drawn.
Therefore, there are losing tickets.
Hence, there are winning tickets, and your probability of winning a super prize is
Note: We can approach this problem using direct counting, but there are a number of cases: 1) Matching 3 white balls with any super ball. 2) Matching 2 white balls with any super ball. 3) Matching 1 white ball and matching the super ball. 4) Matching 0 white balls and matching the super ball.
Given the numerous cases here, a complementary counting approach is a faster approach.
