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Conditional probability: selecting one from a set

  1. Aug 12, 2014 #1
    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
     
  2. jcsd
  3. Aug 12, 2014 #2

    phinds

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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?
     
  4. Aug 12, 2014 #3
    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).
     
  5. Aug 12, 2014 #4

    HallsofIvy

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    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.

    Yes, that is correct. There are a total of 3+ 2= 5 brown dogs and 2 of them are female: 2/5.

    Yes, that is correct, There are a total of 10 female dogs and 2 of them are brown: 2/10= 1/5.

    What answers does your book give?
     
  6. Aug 12, 2014 #5
    Thank you, my book answers are
    1. P=3/22
    2. P=2/5
    3. P=3/10
     
  7. Aug 13, 2014 #6

    haruspex

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    Book's wrong. Can't think of a simple change to the inputs that gives those answers.
     
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