Question

5. A survey of MBA students obtained the following data on “Students’ first reason for application...

5. A survey of MBA students obtained the following data on “Students’ first reason for application to the school in which they matriculated.”

Quality

Cost/Convenience

Other

Full Time

421

393

76

Part-Time

400

593

46

You select a student at random. What is the probability they:
a. Are a full-time student?

b. Chose their school for cost/convenience reasons?

c. Chose their school for quality given that they are a full-time student?

d. Chose their school for quality and are a full-time student?

e. Chose their school for cost/convenience or are a part-time student?

** Please show work
f. Are enrollment status and reason for application independent events? Prove.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1
Quality Cost/Convenience Other Total
Full-time 421 393 76 890
Part-time 400 593 46 1039
Total 821 986 122 1829

(a) The probability that they are a full-time student

= Number of full-time students/Total number of students = 890/1829

= 0.4866

(b) The probability that they chose their school for cost/convenience reasons = 986/1829 = 0.5391

(c) The required probability = P(Quality and Full-time)/P(Full-time)

= 421/890 = 0.4730

(d) The required probability = 421/1829 = 0.2302

(e) The required probability = P(cost/convenience) + P(part time) - P(cost/convenience and part time)

= 986/1829 + 1039/1829 - 593/1829

= 1432/1829 = 0.7829

(f) No, the events enrollment status and reason for application are not independent.

Since P(Student chose their school for quality) = 821/1829 = 0.4489 is not equal to the Probability that a student chose their school for quality given that they are a full-time student.

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