Problem 2. Among Vulcans, there is a trait known as Sehlat Fangus Magma; Vulcans

Question

 Problem 2. Among Vulcans, there is a trait known as Sehlat Fangus Magma; Vulcans with this trait enjoy petting large Sehlats. Note that Sehlats are like live Teddy Bears with fangs.  Those who don't have Sehlat Fangus Magma prefer petting small Sehlats.  As a research geneticist, you perform a study with a sample size of 37 subjects.  The breakdown of individuals by phenotypes is as follows:   2      individuals are   male and        have Sehlat Fangus Magma;   7      individuals are female and        have Sehlat Fangus Magma;   16     individuals are   male and do not have Sehlat Fangus Magma;   12     individuals are female and do not have Sehlat Fangus Magma.  Question A. What is the probability a Vulcan is male?  Question B. What is the probability a Vulcan has Sehlat Fangus Magma and is male?  Question C. What is the probability a Vulcan has Sehlat Fangus Magma given that he is male? 

Explanation / Answer

Total sample size = 37

A) number of male = 2 + 16 = 18

P(a Vulcan is male) = 18/37 = 0.486

B) P(a Vulcan has sehlat fangus magma and is male) = 2/37 = 0.054

C)  P(a Vulcan has sehlat fangus magma | is male) =  P(a Vulcan has sehlat fangus magma and is male) / P(male)

= 0.054/0.486

= 0.111

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