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%