Question

In a university, if a student is a business major, then there is 70% chance that he/she will be employed immediately after graduation. And if a student is not a business major, then there is a 35% chance that hel she will be employed immediately after graduation. We also know that 40% of students are business majors and 60% of students are not business majors. What is the probability that a student is a business major given that he or she is employed immediately after graduaton?

Answer 1

To find the probability that a student is a business major given that they are employed immediately after graduation, we can use Bayes' theorem:

P(Business Major | Employed) = P(Employed | Business Major) * P(Business Major) / P(Employed)

We are given the following probabilities:

P(Employed | Business Major) = 0.70
P(Business Major) = 0.40
P(Employed | Not Business Major) = 0.35
P(Not Business Major) = 0.60

First, we need to find the probability of being employed (P(Employed)):

P(Employed) = P(Employed | Business Major) * P(Business Major) + P(Employed | Not Business Major) * P(Not Business Major)

P(Employed) = (0.70 * 0.40) + (0.35 * 0.60) = 0.28 + 0.21 = 0.49

Now, we can use Bayes' theorem to find the probability that a student is a business major given that they are employed immediately after graduation:

P(Business Major | Employed) = (0.70 * 0.40) / 0.49 ≈ 0.5714

So, the probability that a student is a business major given that they are employed immediately after graduation is approximately 57.14%