Problem 1. Among Romulans, there is a trait known as Reas Romulus Betta; Romulan

Question

 Problem 1. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors.  Those who don't have Reas Romulus Betta do not watch these fish.  You are performing a study with a large population of subjects.  The proportions of individuals with phenotype-pairs is as follows:  The proportion of individuals who are   male and        have Reas Romulus Betta is 0.207;  The proportion of individuals who are female and        have Reas Romulus Betta is 0.0963;  The proportion of individuals who are   male and do not have Reas Romulus Betta is 0.132;  The proportion of individuals who are female and do not have Reas Romulus Betta is 0.565.  Question A. What is the probability a Romulan is male in this population?  Question B. What is the probability a Romulan has Reas Romulus Betta and is male?  Question C. What is the probability a Romulan has Reas Romulus Betta given that he is male? 

Explanation / Answer

A) P(a romulan is male) = P(male and have reas romulan betta) + P(male and do not have reas romulan betta)

= 0.207 + 0.132

= 0.339

B) P( having Romulus betta and male) = 0.207

C) P( having Romulus betta | male) = P( having Romulus betta and male) / P(male)

= 0.207/0.339

= 0.796

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