Conditional probability: selecting one from a set

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Discussion Overview

The discussion revolves around calculating conditional probabilities related to selecting dogs from a specified group. Participants explore the probabilities of selecting female brown dogs and the relationships between different categories of dogs based on gender and color.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a scenario with a group of dogs and asks for the probabilities of selecting a female brown dog, selecting a female given that the dog is brown, and selecting a brown dog given that the dog is female.
  • Another participant confirms the calculations of the first participant, agreeing with the probabilities derived for each case.
  • A later reply questions the correctness of the book's answers, suggesting that the book's probabilities do not align with the calculations provided by the participants.
  • One participant reiterates the book's answers, which differ from their own calculations, specifically noting discrepancies in the probability of selecting a female brown dog and the probability of selecting a brown dog given that the dog is female.
  • Some participants express uncertainty about how to reconcile the differences between their calculations and the book's answers.

Areas of Agreement / Disagreement

Participants generally agree on the calculations provided for the probabilities, but there is disagreement regarding the correctness of the book's answers, which some participants believe are incorrect.

Contextual Notes

Participants rely on specific counts of dogs and their classifications, which may lead to different interpretations based on how probabilities are calculated or defined. The discussion does not resolve the discrepancies with the book's answers.

Medicol
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I have a group of dogs (3 brown male, 2 brown female, 4 white male, 4 white female, 5 black male, 4 black female)
What is the probability to
1. select a female brown dog ?
2. select a female, given that is a brown dog ?
3. select a brown given that is a female dog ?

Thank you.

I have tried

1. P(BrB)=freq of female brown/total dog number=1/11
2. P(F , Br)=P(female brown)/P(brown)=1/11 / 5/22 = 2/5
3. P(Br, F) = P(female brown)/P(female)=1/11 / 10/22 = 1/5


But my answers are different from those in my book
 
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Let's say you have 10,000,000 marbles in a REALLY big jar. All but 3 of them are blank and pure black. The three are all white and one of them has a 1 printed on it, one of them a 2 and one of them a 3. You draw a ball and it is white. What are the odds that it has a 1 printed on it?
 
Your answers look OK to me, what does the book say?

Note that we usually write "probability of brown given female" as P(Br|F).
 
Medicol said:
I have a group of dogs (3 brown male, 2 brown female, 4 white male, 4 white female, 5 black male, 4 black female)
What is the probability to
1. select a female brown dog ?
2. select a female, given that is a brown dog ?
3. select a brown given that is a female dog ?

Thank you.

I have tried

1. P(BrB)=freq of female brown/total dog number=1/11.
Yes, this is correct. There are a total of 3+ 2+ 4+ 4+ 5+ 4= 22 dogs and 2 of them are brown females: 2/22= 1/11.

2. P(F , Br)=P(female brown)/P(brown)=1/11 / 5/22 = 2/5
Yes, that is correct. There are a total of 3+ 2= 5 brown dogs and 2 of them are female: 2/5.

3. P(Br, F) = P(female brown)/P(female)=1/11 / 10/22 = 1/5
Yes, that is correct, There are a total of 10 female dogs and 2 of them are brown: 2/10= 1/5.

But my answers are different from those in my book
What answers does your book give?
 
Thank you, my book answers are
1. P=3/22
2. P=2/5
3. P=3/10
 
Medicol said:
Thank you, my book answers are
1. P=3/22
2. P=2/5
3. P=3/10
Book's wrong. Can't think of a simple change to the inputs that gives those answers.
 

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