8. Given the following survey results of 100 randomly selected graduate economic

Question

8. Given the following survey results of 100 randomly selected graduate economics students at Kim Il Sung University, North Korea, determine the following probabilities. [Hint: Complement rule and additive rule for independent events]

50 students are taking Professor Marx’s course Das Kapital

60 students are taking Professor Smith’s course Wealth of Nations

10 students are not taking either professor’s course

8.1   A student takes Professor Smith’s course given that he/she takes Professor Marx’s course

8.2   A student takes Professor Marx’s course given that he/she does not take Professor Smith’s course

8.3   A student takes one but not both professors’ courses

Please explain how you aquired your answer, and if you used a TI-83 or 84 calculator please explain what you did on it.

Thank you.

Explanation / Answer

8. From information given, P(students taking Marx's)=50/100=0.5, P(students taking Smith's)=60/100=0.6, P( students taking Marx's course intersection Smith's course)'=10/100=0.1. Therefore, P( students taking Marx's course union Smith's course)=1-0.1=0.9 [Apply, P(A)=1-P(A)']. Substitute the values in following formula to compute P( students taking Marx's course intersection Smith's course).

P( students taking Marx's course intersection Smith's course)=P(student taking Marx's course)+P(student taking Smith's course)-P( students taking Marx's course union Smith's course)

=0.5+0.6-0.9=0.2 [Apply, P(A U B)=P(A)+P(B)-P(A intersection B)]

8.1 P(a student takes Smith's course| student takes Marx's course)=P( students taking Marx's course intersection Smith's course)/P(student takes Marx's course)

=0.2/0.5

=0.4

8.2.

P(a student takes Marx's course| student takes Smith's course)=P( students taking Marx's course intersection Smith's course)/P(student takes Smith's course)

=0.2/0.6

=0.33

8.3 Probability of a student taking Smith's course but not Marx's course is: P(Smith intersection Marx')=P(Smith)-P(Smith's intersection Marx's)=0.6-0.2=0.4

Probability that a student taking Marx's course but not Smith's is: P(Marx's intersection Smith's)=P(Marx's)-P(Smith's intersection Marx's)=0.5-0.2=0.3

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