Problem 6. Among Romulans, there is a trait known as Reas Romulus Betta; Romulan
ID: 3203251 • Letter: P
Question
Problem 6. 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 0.0104; The proportion of individuals who are female and have Reas Romulus Betta is 0.417; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.386; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.187. 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. 417+ 0.187
= 0.604
b) Probability not have reas romulan betta and female = P(F|RB) = 0.187
c) P(RB|F) = [P(F|RB) * P(RB)] / [P((F|RB) * P(RB) + P(F|RA) * P(RA)]
P(RA) = 0.0104+ 0.417 = 0.4274
P(RB) = 0.386 + 0.187= 0.573
P(F|RB) = 0.187
P(F|RA) = 0.417
= (0.187 * 0.573 ) / (0.187 * 0.573 + 0.417 * 0.4274)
= 0.375