Question

In the college of business at Lewis university, 40% of students enroll in a business analytics major. 30% in a finance major, 20% in a project management major, and 10% in an organizational leadership major. If a student enrolls in a business analytics major, he/she has a 70% chance of finding a job in the first month of graduation. If a student enrolls in a finance major, he/she has a 60% chance of finding a job in the first month of graduation. If a student enrolls in a project management major, he/she has a 50% chance of finding a job in the first month of graduation. If a student enrolls in an organizational leadership major, he/she has a 40% chance of finding a job in the first month of graduation. What is the probability that a student is a business analytics major, given that he/she finds a job in the first month of graduation?

Answer 1

0.47

Explanation:

Given Information

`P(BA)=0.4\\P(F)=0.3\\P(PM)=0.2\\P(OL)=0.1\\\\P(\text{Job}|BA)=0.70\\P(\text{Job}|F)=0.60\\P(\text{Job}|PM)=0.50\\P(\text{Job}|OL)=0.40`

Calculation with Bayes' Theorem

`\displaystyle P(BA|\text{Job})=\frac{P(\text{Job}|BA)P(BA)}{P(\text{Job})}\\\\P(BA|\text{Job})=\frac{P(\text{Job}|BA)P(BA)}{P(\text{Job}|BA)P(BA)+P(\text{Job}|F)P(F)+P(\text{Job}|PM)P(PM)+P(\text{Job}|OL)P(OL)}\\\\P(BA|\text{Job})=((0.70)(0.40))/((0.70)(0.40)+(0.60)(0.30)+(0.50)(0.20)+(0.40)(0.10))\\\\P(BA|\text{Job})=(0.28)/(0.28+0.18+0.10+0.04)\\\\P(BA|\text{Job})=(0.28)/(0.60)\\\\P(BA|\text{Job})\approx0.47`

Therefore, the probability that a student is a business analytics major, given that he/she finds a job in the first month of graduation is about 0.47.