Posterior Probability and Independence Problem: Bayes Theore

[pfeiferm]

I have a homework problem that I cannot figure out, I don't even know where to begin on this problem:

An island has three species of bird. Species 1 accounts for 45% of the birds, of which 10% have been tagged. Species 2 accounts for 38% of the bifds, of which 15% have been tagged. Species 3 accounts for 17% of the birds of which 50 have been tagged. If a tagged bird is observed, what are the probabilities that it is of species 1, of species 2, and of species 3?

I assume that if I undestand how to slove for species 1, I can do the other 2 by myself. I think I am suppposed to use Bayes' Theorem, since we covered that in this chapter of the book. Thanks for the help.

 

[galactus]

Did you mean 17% of species 3, of which 50% are tagged?.

Anyway, that is what I went with. ! used 1000 birds as a base value. You can use whatever you like. 1000 is a nice number easy to work with.

Build a chart:

                     1                                       2                        3                     total
----------------------------------------------------------------------------------------------------------------
TAGGED                45                                     57                        85                187

NOT TAG              405                                    323                       85                813
--------------------------------------------------------------------------------------------------------------
                        450                               380                       170                  1000

Now, you can answer whatever you like. For instance, What is the probability a bird is tagged given it came from species 1?.

45/450=1/10

What is the probability a bird comes from species 3 given it is not tagged?.

85/813.

And so on.