I need help calculating the conditional probability of this problem (b) Imagine

Question

I need help calculating the conditional probability of this problem

(b) Imagine a study that observed 200 female birds. Of these, 20 females chose a genetically poor mate. Imagine further that of the females paired with genetically poor mates, 18 engaged in extra-pair copulation; and of the females paired with a genetically high-quality mate, 90 engaged in extra-pair copulation. Calculate the overall probability of extra-pair copulations, and the probability of engaging in extra-pair copulation, conditional on primary mate choice (show your math, not just the end result). (2 Points)

Explanation / Answer

b)probability of extra pair copulation =P(genetically poor mate and extra pair copulation) +P(genetically high quality mate and extra pair copulation)  

=(20/200)*(18/20)+(180/200)*(90/180)=0.54

probability of engaging in  extra pair copulation conditioned on poor mate choice =N(genetically poor mate and extra pair copulation)/N( poor mate choice) =18/20=0.9

probability of engaging in  extra pair copulation conditioned on poor mate choice =N(genetically high quality mate and extra pair copulation)/N( high quality mate choice) =90/180=0.5

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