Each adult carries TWO alleles for egg color. If the female lays "pink" eggs then she is carrying at least one allele for brown (pink is a shade of brown). She is not carrying any alleles for blue because if she were her eggs would not be "pink", they would be green. It is possible therefore that she has two alleles for brown or one for brown and one for white.
The rooster is an unknown because he doesn't lay eggs
But let's assume he would be a green egg layer. That would mean he carries one allele for brown and one for blue.
Predicting egg colors for the offspring of this mating can be done with a classic Punnett square. The possible combinations are as follows:
brown, brown = brown or pink eggs 50%
brown, blue = green eggs 50%
OR( if she has one white allele)
brown, brown = brown or pink eggs 25%
brown blue = green eggs 25%
white, brown = brown or pink eggs 25%
white, blue = blue eggs 25%
There are two possible allele combinations in this scenario resulting in a brown/pink egg resulting in a total probability of 50% for that color.
My understanding is that the shade of color (how deep it is) is dependent on a number of modifiers. I've also heard that the allele for blue egg color is additive so that a hen with two alleles for blue will lay eggs that are more blue than if she only had one copy.