Question

Students taking the GMAT were asked about their undergraduate major and pursuit of their MBA as full time or part time student,

	Business	Engineering	Other	Total
Full Time	352	197	251	800
Part Time	150	161	194	505
Total	502	358	445	1305

If a student taking the GMAT is randomly selected from this distribution find:

1. The probability that their undergraduate major was business.
2. The probability that their undergraduate major was not business.
3. The probability that their undergraduate major was business and they are a part time student.
4. The probability that their undergraduate major was business or they are a part time student.
5. The probability that they are in business given that they are a part time student.
6. The probability that they are a part time student given that they are in business.

Answer 1

a) P(Business) = 502 / 1305 = 0.385

b) P(not business) = 1 - P(business) = 1 - 0.385 = 0.615

c) P(business and part time student) = 150 / 1305 = 0.115

d) P(business or part time student) = P(business) + P(part time student) - P(business and part time student)

                                                        = 502/1305 + 505/1305 - 150/1305

                                                        = 0.657

e) P(business | part time student) = P(business and part time student) / P(part time student)

                                                      = (150/1305) / (505/1305)

                                                      = 150 / 505

                                                      = 0.297

f) P(part time student | business) = P(business and part time student) / P(business)

                                                     = (150/1305) / (502/1305)

                                                     = 150 / 502

                                                     = 0.299