Problem 4. Among Romulans, there is a trait known as Reas Romulus Betta; Romulan

Question

 Problem 4. 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 0.0567;  The proportion of individuals who are female and        have Reas Romulus Betta is 0.269;  The proportion of individuals who are   male and do not have Reas Romulus Betta is 0.207;  The proportion of individuals who are female and do not have Reas Romulus Betta is 0.468.  Question A. What is the probability a Romulan is female in this population?  Question B. What is the probability a Romulan does not have Reas Romulus Betta and is female?  Question C. What is the probability a Romulan does not have Reas Romulus Betta given that she is female? 

Explanation / Answer

P(RA) = Romulan with read romulan betta

P(F) = Probability of female

P(RB) = Romulan without read romulan betta

P(M) = Probability of male

a) Probability of romiulan female = P(F|RA) + P(F|RB)

= 0.269 + 0.468

= 0.737

b) Probability not have reas romulan betta and female = P(F|RB) = 0.468

c) P(RB|F) = [P(F|RB) * P(RB)] / [P((F|RB) * P(RB) + P(F|RA) * P(RA)]

P(RA) = 0.0567 + 0.269 = 0.3257

P(RB) = 0.207 + 0.468 = 0.675

P(F|RB) = 0.468

P(F|RA) = 0.269

= (0.468 * 0.675) / (0.468 * 0.675 + 0.269 * 0.3257)

= 0.78

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