Question

A campus has 55% male students. Suppose 30% of the male students pick basketball as their favorite sports compared to 20% for females. If a randomly chosen student picks basketball as the student’s favorite sport, what is the probability the student is male?
A.

.30 / 30 + .20

B. 

.55 / .30 + .20

C..30 / (.55)(.30) + (.45)(.20) D.
.55 / (.55)(.30) + (.45).(20) E. (.55)(.30) / (.55)(.30) + (.45)(.20)      

PROVIDE EXPLANATION

Answer 1

This is question of probability finding using bayes theorem  
It is used to calculate probability of two competing statements 
now p(m) = .55 
p(~m)= .45 
now for basketball for male  
p(b|m)=.30
 and for female 
p(b|~m)=.20 
so by bayes theorem  
p(m|b)=p(b|m)*p(m)/(p(b|m)*p(m)+p(b|~m)*p(~m)) 
so answer is E 
(.55)(.30) / (.55)(.30) + (.45)(.20)