Among the students registered in Econ 200, 30% are social science majors, 20% ar

Question

Among the students registered in Econ 200, 30% are social science majors, 20% are business majors, and the remaining 50% are other majors. Among each of these groups, 40% are first year students, 30% are second year students and the remaining 30% are upper year students. a) Define which events are mutually exclusive. b) What is the probability that a randomly chosen student is a second year business major? c) What is the probability that a randomly chosen student is either a second year, or a business major (he/she could be both)?

Explanation / Answer

a. Mutual exclusive events:

type1: students chosen from two different majors

type 2: students chosen from two different years

type 3: a combination of both eg. intersection of students belonging to social science 1st yr and business 2nd yr is 0

b. prob = prob that the student is a business major* prob that the student is in 2nd yr

= 20%*30% = 6%

c. prob = prob(2nd yr) + prob(business major) - prob(both)

= 30% + 20% - 6% (from prev answer)

= 44%

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