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.

Answer 1

0.9398 = 93.98% probability that the student is not of Asian origin.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Business student

Event B: Not of Asian origin.

Probability that the student is an undergraduate majoring in business.

15% of 13%(Of Asian origin).

35% of 100 - 13 = 87%(Not of Asian origin). So

`P(A) = 0.15*0.13 + 0.35*0.87 = 0.324`

Business student and not of Asian origin:

35% of 87%. So

`P(A \cap B) = 0.35*0.87 = 0.3045`

One undergraduate student majoring in Business is randomly selected from this university. Find the probability that the student is not of Asian origin.

`P(B|A) = (P(A \cap B))/(P(A)) = (0.3045)/(0.324) = 0.9398`

0.9398 = 93.98% probability that the student is not of Asian origin.