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 a prize, the numbers on your ticket must match at least two of the white balls or must match the SuperBall.

**If you buy a ticket, what is your probability of winning a prize?**

AnimalMaster Feb 6, 2020

#1**0 **

Case 1: Superball

The probability is 1/10, because you choose 1 out of 10.

Case 2: 2 whites

The probability is 1/C(10,2) = 1/45, because you choose 2 out of 10.

Case 3: 3 whites

The probability is 1/C(10,3) = 1/120, because you choose 3 out of 10.

Adding these, you get 1/10 + 1/45 + 1/120 = 47/360.

Guest Feb 6, 2020

#4**+2 **

In the Small State 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 a prize, the numbers on your ticket must match at least two of the white balls or must match the SuperBall.

When you buy a ticket, you select three numbers from 1-10 the numbers on your ticket must match at least two of the white balls

Here is the logic, I expect if you work through it properly you will find the answer to this bit.

https://nihilistslab.com/html/products/engb/kinostatistics/MathematicalAnalysisOfKeno.html

I've decided to answer further but I have not fully worked out the logic behind this formula and the rest is a half guess as well.

The number of ways that 3 numbers can be chosen from 10 is 10C3 = 120 this is the sample space.

The number of ways that 3 numbers can be chosen from 10 and 2 of them match the original 3 chosen is

3C2 * (10-3)C(3-2) = 3*7 = 21

The number of ways that 3 numbers can be chosen from 10 and 3 of them match the original 3 chosen is 1

So that is 22 ways that the numbers can do it irrespective of the superball.

so that is \(\frac{22}{120}=\frac{110}{600}\)

120-22 = 98 ways where the numbers will not work so the superball is needed.

98/120 * 1/10 =

\(\frac{98}{120}*\frac{1}{10}=\frac{98}{1200}=\frac{49}{600}\)

So maybe the probability is \(\frac{110+49}{600}=\frac{159}{600}\)

I am very dubious about the accuracy of this but at present, it is my best guess.

If you find out the 'real' answer then please share it with the rest of us.

Melody Feb 9, 2020