A scientist performs an experiment to test two hypothesis. If hypothesis A is correct, there is a 20% chance that the experiment succeeds. If hypothesis B is correct, there is a 100% chance that the experiment succeeds. The two hypothesis are mutually exclusive, and one of them is definitely correct. If the experiment does in fact succeed, what are the chances that hypothesis A is the correct one?

I don't know if I did this correctly, but I did

P(B)=P(A')

P(C|A)=.2

P(C|B)=1

P(A|C)=P(AnC)/P(C)

=P(C|A)*P(A)/P(C)

P(C)=P(C|A)*P(A)+P(C|B)*P(B)

P(A|C)=(P(C|A)*P(A))/(P(C|A)*P(A)+P(C|B)*P(B))

=.2P(A)/(1-.8P(A))

Here's where I get mixed up. I don't know whether or not to say that hypothesis A and B are initially equally likely, and set P(A)=P(B)=.5. If I do, then

P(A|C)=.2*.5/(1-.8*.5)

=1/6

But I don't know whether or not I can do that. It seems like a really arbitrary thing to do. Could somebody out there help me please? This is really bothering me. Thanks!