What is the probability of two seeds germinating if their types are unknown?

[permorten]

Let the germination probability (the probability that a seed sprouts) for seed A be Pa and B be Pb.


a) You plant two seeds of the same kind. If you turn heads or tails of what sort you plantet, what is the probability that 2 seeds germinate?
b) A student plant 2 seeds, but he had forgotten to note what sort of seed he had planted. What is the probability that it was A if both germinate?

What i think i right so far:

a) probability should be: P = (Pa^2+Pb^2)/2

 

[Some Pig]

b) P(A|2 germinate)
=P(2 germinate|A)P(A)/P(2 germinate)
$$=\frac{\frac12P_a^2}{\frac12(P_a^2+P_b^2)}=\frac{P_a^2}{P_a^2+P_b^2}.$$