Statistics

EXAMPLE:

A law school is looking at the effectiveness of a particular Bar preparation class. They looked at 150

recent graduates and found that 100 failed the Bar exam on their first attempt. They also determined

that 40 of the students who completed the Bar-prep class passed on their first attempt.

The school completed a contingency table based on their analysis. Use the information in the table to

discuss the following questions.

Does knowing if a graduate has completed the class help the school predict how likely the graduate is to

pass the Bar Exam on the first try?

Why?

What does you answer imply about the statistical relationship between completing the class and passing

the Bar Exam?

Use the relationship between Marginal, Joint and Conditional probability from this week's lesson to

justify your answers.

INITIAL POST

Knowing that the graduate completed the Bar-prep class does help the school predict if graduates will

pass the Bar exam on the first attempt.

If completing the class affects the probability of passing the Bar Exam on the first attempt, then the

Conditional Probability of Passing, given completing the class, P(Passing | Completed) will be different

than the Marginal Probability of Passing P(Passing).P(Passing) = 50/150 = 0.333

P(Passing | Completed) = P(Passing AND Completed) / P(Completed)

P(Passing | Completed) = (40/150) / (69/150) = 0.580

Complete

Bar-prep

Class

No Bar-prep

Class Total

Passed

the Bar 40 10 50

Failed the

Bar 29 71 100

Total 69 81 150

Knowing that a graduate completed the Bar-prep class increased their probability of passing the Bar

Exam on the first attempt from 33.3% to 58.0%.

Since the outcome of one event (completing the class) affects the probability of the second event

(passing the Bar on the first try) the two events are not independent. We can confirm this by using the

Multiplication Rule, which states: “If A and B are independent, the probability of A AND B is equal to the

probability of A times the probability of B.

P(Passing) = 50/150 = 0.333

P(Completed) = 69/150 = 0.460

P(Passing) * P(Completed) = 0.333 * 0.460 = 0.153

P(Passing AND Completed) = 40/150 =0.267

P(Passing AND Completed) ≠ P(Passing) * P(Completed) so the two events are not independent