What Is the Probability Ely Eats 16 Chocolates Without Picking a Rum One?

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Homework Help Overview

The problem involves calculating the probability that Ely consumes 16 chocolates without picking a rum-flavored one, given a specific dietary constraint and a box of chocolates with multiple flavors. The context is rooted in basic probability principles.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the probability of selecting non-rum chocolates and the implications of Ely's dietary restrictions. There are mentions of different probability distributions, including binomial and hypergeometric, as well as the process of calculating probabilities through multiplication of fractions.

Discussion Status

The discussion is active, with participants exploring various methods to approach the problem. Some have suggested using binomial coefficients, while others have shared their attempts at manual calculations. There is no explicit consensus on a single method, but productive dialogue is occurring.

Contextual Notes

Participants are working under the assumption that Ely can consume up to 16 chocolates without exceeding her calorie limit, and they are considering the implications of the chocolate flavors available in the box.

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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?



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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.
 
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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?
 
what is it 1.4% that you reach by multiplying it out?
 
Yes, that's it. Can you write it in terms of binomial coefficients?
 
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?
 
Centurion1 said:
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.
 
Thank you for your help!