2 Coops and Chickens problem

[Warrior]

Hi,

I have a question as homework to solve, but although it's so easy (as everyone says) I am not still able to solve it. Could you please help me with that?

We have two coops: in coop 1 there are 10 male and 5 female chickens. Coop 2 has 5 male and 10 female chickens. We randomly select two chickens from coop 1 and move then to coop 2.

Q1: Now we randomly select 1 chicken from coop 2 and take it out. What is the probability that it's a female?
Q2: We randomly select another chicken and take it out. What is the probability that the second one is also a female given that the first one was a female?

Thank you

 

[Dason]

Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

 

[Warrior]

Hi and welcome to myself

Here's what I think as of now:

There are four possible ways of taking two chickens out of coop 1 and put them in coop 2 as follow: {Male-Male, Female-Female, Male-Female, Female-Male}. However, I get a confused for the first question because of those four possible selections, the chance of the taken off chicken to be female might be either 10/17, 11/17 or 12/17. So, this is where I am lost as of now. Any clue?

 

[Dason]

Well it looks like you can tell me the probability that any of those four possibilities occurs. And it looks like you can tell me that if you knew which of the possibilities actually happened then you could tell me the probability of selecting a female - correct?

You might consider what the Law of total probability has to say about the overall probability of selecting a female would be in this case.

 

[Warrior]

The probabilities are as follow:

1- Male-Male: 10/15, 9/14
2- Female-Female: 5/15, 4/14
3- Male-Female: 10/15, 5/14
4- Female-Male: 5/15, 10/14

If 1 has happened the probability of the chicken taken off will be 10/17.
If 2 has happened the probability of the chicken taken off will be 12/17.
If 3 has happened the probability of the chicken taken off will be 11/17.
If 4 has happened the probability of the chicken taken off will be 11/17.

Am I correct so far?
However I still don't get how I shall correlate the probabilities above (in this post) to the probabilities of selecting a female from coop 2.

Do I need to use the example given in the Law of total probabilities page on Wikipedia for this problem?