So I saw someone post this question, and I saw the solution that I didn't understand: https://web2.0calc.com/questions/extremely-tricky. It said that the probability should be closer to 1/4. But why? Also, I don't know how to solve this problem.

In the SmallState Lottery, three white balls are drawn (at random) from ten balls numbered 1 through 10, and a blue SuperBall is drawn (at random) from ten balls numbered 11 through 20. When you buy a ticket, you select three numbers from 1-10 and one number from 11-20. To win the jackpot, the numbers on your ticket must match the three white balls and the SuperBall. (You don't need to match the white balls in order).

If you buy a ticket, what is your probability of winning the jackpot?

Guest Feb 5, 2020

#1**+2 **

To find the probability of the three white balls:

You have to select all of the winning balls; in other words, you have to select three winning balls from three winning balls, and this can be done in _{3}C_{3} ways (which is just 1 way).

You also have to select none of the losing balls, in other words, you have to select zero losing balls from seven losing balls, and this can be done in _{7}C_{0} ways (which, also, is just 1 way).

Then, you have to divide this result from the total number of ways that 3 balls can be drawn from 10 balls, and this can be done in _{10}C_{3} ways (which is 120 ways).

Summarizing: [ _{3}C_{3} · _{7}C_{0} ] / _{10}C_{3} = 1 · 1 / 120 = 1/120.

You also have to select the SuperBall. Since there are 10 possibilities and you must select the 1 that is the winner, your probability of selecting the SuperBall is 1/10.

Your probability of selecting all three white balls and the SuperBall is: (1/120) · (1/10) = 1/1200.

geno3141 Feb 6, 2020