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

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In summary, 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
  • #1
Centurion1
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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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  • #2
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?
 
  • #3
what is it 1.4% that you reach by multiplying it out?
 
  • #4
Yes, that's it. Can you write it in terms of binomial coefficients?
 
  • #5
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?
 
  • #6
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.
 
  • #7
Thank you for your help!
 

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

What is probability?

Probability is a measure of the likelihood or chance that a specific event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and predicts the likelihood of an event occurring. Experimental probability is based on actual observations and data collected from experiments or real-life situations.

How do you calculate probability?

To calculate probability, divide the number of favorable outcomes by the total number of possible outcomes. This will give you a decimal value, which can be converted to a percentage by multiplying by 100.

What is the difference between independent and dependent events?

Independent events are events whose outcomes do not affect each other. For example, flipping a coin twice would be an example of independent events. Dependent events are events whose outcomes are affected by previous events. For example, drawing two cards from a deck without replacement would be an example of dependent events.

How can probability be used in real life?

Probability can be used in real life to make predictions and informed decisions. It can help in fields such as finance, insurance, and medicine to calculate risk and make strategic choices. It can also be used in games of chance, such as gambling, to understand the likelihood of winning or losing.

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