# Probability: Bayes Theorem

An admissions committee must select students for an MBA program. Past data show that 70% of students complete (C) the program. It is also known that 50% of the graduating students scored above 500 (A) on the GMAT test. While 20% of the dropouts (D) scored that well. Consider a new MBA student.

A) What is the prior probabilty that she will complete the degree

B) Given that she scores 575 on the GMAT test, what is posterior probability that she will complete her MBA

C) Given that she scores 450 on the test, what is the posterior probability that she will graduate?

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#### Solution Preview

% that graduate= 70%

% of Dropouts= 30%

Total= 100%

A) What is the prior probability that she will complete the degree

Probability is = 70% or 7/10

Answer: 7/10

B) Given that she scores 575 on the GMAT test, what is posterior probability that she will complete her MBA

Let the no of students be = 100

No that graduate= 70 =70.%*100

No of dropouts= 30 =30.%*100

% of graduating students that score over 500 in GMAT= 50%

No of graduating students who scored more than 500 in GMAT= 35 =50.%*70

% of dropouts that score over 500 in GMAT= 20%

No of dropouts who scored more than 500 in ...

#### Solution Summary

Solves a probability question using Bayes theorem.