# Conditional probability: selecting one from a set

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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phinds
Gold Member
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?

pbuk
Gold Member

Note that we usually write "probability of brown given female" as P(Br|F).

HallsofIvy
Homework Helper
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

Thank you, my book answers are
1. P=3/22
2. P=2/5
3. P=3/10

haruspex