Basic Probability Question

[Centurion1]

Homework Statement

1. Ely is on a 1000-calorie/day diet which she has been strictly following for about 2 weeks now. Thelma, her college buddy, is in town, though, and she has brought with her Ely’s favorite chocolate from their college town. Ely has a real weakness for chocolates and she will eat any type as long as it does not have any liquor in it. If Thelma brought a box of thirty indistinguishable chocolate nuggets (each one having 50 calories) and there are equal amounts of the 6 flavors—orange, hazelnut, rum, strawberry, almond and praline—what is the probability that she will consume 80% of her calorie allowance for the day on Thelma’s chocolates before she gets a rum-flavored chocolate?

Homework Equations

The Attempt at a Solution

Right so I know that the chances of getting a rum chocolate are at 17% to start off. And thne with each chocolate taken it decreases accordingly; i.e. 5/29, 5/28, etc. And that ely can take 16 chocolates before she goes over her diet

But I am not sure how to put it all together. I am not really looking for the blatant answer but more the process to find the answer. Obviously this is very basic probability and the actual math is not challenging.

 

[vela]

You want to think about the probability of not choosing a rum chocolate. For her to consume 80% of her calorie limit, she has to choose 16 non-rum chocolates. What's the probability of doing so?

 

[Centurion1]

what is it 1.4% that you reach by multiplying it out?

 

[vela]

Yes, that's it. Can you write it in terms of binomial coefficients?

 

[Centurion1]

well i actually did a hypergeometric.

but otherwise multiplying it out manually it is like

25/30 * 24/29 * 23/28 etc. until you do 16 trials.

im going to be asking another question in a different thread which i hope is okay?

 

[vela]

well i actually did a hypergeometric.

Good! That's what I was trying to get at but I can never remember the name of the distribution.

 

[Centurion1]

Thank you for your help!