Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is female given that the employee is a salaried member of staff?
A).167
B).500
C).625
D)267
E).375

Question

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random what is the probability that the employee is female given that the employee is a salaried member of staff?
A).167 
B).500 
C).625 
D)267 
E).375

Quizplus · Accepted Answer

To find the probability that the employee is female given that the employee is a salaried member of staff, we need to use conditional probability.

Let F be the event that the employee is female and S be the event that the employee is salaried. Then we need to find P(F|S), which represents the probability of F given S.

P(F|S) = P(F and S) / P(S)

From the given table, we can see that there are 90 salaried members of staff, out of which 30 are female. So, P(F and S) = 30/200 = 0.15.

Also, there are a total of 120 female employees, out of which 30 are salaried. So, P(S) = 90/200 = 0.45.

Therefore, P(F|S) = 0.15/0.45 = 0.625.

Hence, the best choice is C) .625.

Employees of a Local University Have Been Classified According to Gender