What is the probability that a manager has some business education, given that he has some engineering education?

Question

A study showed that 60% of manager had some business education and 55% had some engineering education. Furthermore, 25% of the mangers had some business education but no engineering education. What is the probability that a manager has some business education, given that he has some engineering education?

Answer 1

Let E₁ = Manger has some business education and E₂ = Manager has some engineering education

P(E₁) = 60% = 60/100 = 3/5

and P(E₂) = 55% = 55/100 = 11/20

Also, given that 25% managers has some business education but no engineering education.

\(\therefore\) P(E₁ - E₂) = 25% = 25/100 = 1/4

Now, P(E₁) = P(E₁ - E₂) + P(E₁ ∩ E₂)

\(\therefore\) P(E₁ ∩ E₂) = P(E₁) - P(E₁ - E₂) 

= 3/5 - 1/4 = (12 - 5)/20 = 7/20.

Now, Probability that a manager has some business education given that he has some engineering education is

P(E₁/E₂) = P(E₁ ∩ E₂)/P(E₂) = \(\frac{7/20}{11/20}\) = 7/11