# Probability question on soft-drink machine

1. Jul 6, 2009

### cse63146

1. The problem statement, all variables and given/known data

A soft-drink machine dispenses only regular Coke and Diet Coke. 60 percent of all purchases from this machine are diet drinks. The machine currently has 10 cans of each type. If 15 customers want to purchase drinks prior to the machine being restocked, what is the prob that each of the 15 is able to purchase the type of drink desired?

2. Relevant equations

Binomial distribution

3. The attempt at a solution

I think it's a binomial distribution. So - 20C15*(0.6)^15*(0.4)^5?

But it doesnt seem right.

Any ideas? Thanks.

Last edited: Jul 6, 2009
2. Jul 6, 2009

### queenofbabes

You want a probability, while what you have is clearly much greater than 1. (I'm sorry, I don't know what you were trying to do)

Surely the first 10 people can buy whatever they want right? What about the 11th? And the 12th?

There probably is a shortcut, but I would consider the 11th-15th people separately, and add them all up.

3. Jul 7, 2009

### HallsofIvy

No, it is NOT "clearly much greater then 1". In fact it is about 0.07465.

4. Jul 7, 2009

### queenofbabes

Hey, he edited it at some point >.<

5. Jul 7, 2009

### cse63146

I edited a few typos. The equation I did not touch.

But I got the anwers anyways.

6. Jul 13, 2009

### cse63146

would it have been possible to do it through the hypogeometric distribution?

7. Jul 14, 2009

### cse63146

Thanks, I did it through the hypogeometric distribution.