At a state university on the west coast, 13% of undergraduate students are of As

Question

At a state university on the west coast, 13% of undergraduate students are of Asian origin. Among students of Asian origin, 11% major in Humanities, 7% in Social Sciences, 31% in Biological and Physical Sciences, 36% in engineering, and the remaining 15% in Business. Among students of other ethnicities, 19% major in Humanities, 16% in Social Sciences, 12% in Biological and Physical Sciences, 18% in engineering, and the remaining 35% in Business. One undergraduate student majoring in Business is randomly selected from this university. Find the probability that the student is not of Asian origin.

Explanation / Answer

Probability that the student is of Asian origin = P(A) = 0.13

Probability that the student is not of Asian origin = P(~A) = 1 - P(A) = 1 - 0.13 = 0.87

Given, a student of Asian origin, probability that the student is of Business major = 0.15

That is, P(B | A) = 0.15

Given, a student of non-Asian origin, probability that the student is of Business major = 0.35

That is, P(B | ~A) = 0.35

By law of total probability,

Probability that a student is majoring in Business =

P(B) = P(A) * P(B | A) +  P(~A) * P(B | ~A)

= 0.13 * 0.15 + 0.87 * 0.35

= 0.324

Given, student majoring in Business probability that the student is not of Asian origin

= P(~A | B)

= P(B | ~A) * P(~A) / P(B) (By Bayes theorem)

= 0.35 * 0.87 / 0.324

= 0.9398148

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