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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? |
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Answer» 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 |
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