SOLUTION: Out of 300 applicants for the MPH program, 212 are female and 110 are female and have a nursing degree. If 152 of the applicants to the MPH program have nursing degrees, what is t

Algebra ->  Probability-and-statistics -> SOLUTION: Out of 300 applicants for the MPH program, 212 are female and 110 are female and have a nursing degree. If 152 of the applicants to the MPH program have nursing degrees, what is t      Log On


   

Question 1014264: Out of 300 applicants for the MPH program, 212 are female and 110 are female and have a nursing degree. If 152 of the applicants to the MPH program have nursing degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a nursing degree?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f = number of females = 212
f and n = number of females who have a nursing degree = 110
t = total number of applicants = 300
n = number of applicants who have a nursing degree = 152

p(f) = 212/300
p(f and n) = 110/300
p(n) = 152/300

p(f given n) = p(f and n) / p(n) = (110/300) / (152/300) = 110/300 * 300/152 = 110/152 = .7236842105

this is reasonable since there are 110 females who have a nursing degree out of 152 total applicants who have a nursing degrees.

if you are given that the applicant has a nursing degree, then your universe is 152 applicants who have nursing degrees.

since there are 110 females who have a nursing degree, then the probability of an applicant with a nursing degree being female is 110/152.