Question

a researcher randomly surveyed 122 college professors to determine what types of courses they teach and their sleeping habits. the two - way table displays the data.

suppose a survey respondent is randomly selected. let ( m = ) professor teaches math and ( b = ) professor is an early bird. what is the value of ( p(b|m) )?

( \frac{17}{63} )
( \frac{16}{59} )

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(B|M)=\frac{P(B\cap M)}{P(M)}\). In the context of a two - way table, \(P(B\cap M)=\frac{\text{Number of professors who teach Math and are Early Birds}}{\text{Total number of professors}}\) and \(P(M)=\frac{\text{Number of professors who teach Math}}{\text{Total number of professors}}\). So, \(P(B|M)=\frac{\text{Number of professors who teach Math and are Early Birds}}{\text{Number of professors who teach Math}}\)

Step2: Identify the values from the table

From the table, the number of professors who teach Math and are Early Birds (\(n(M\cap B)\)) is \(16\), and the number of professors who teach Math (\(n(M)\)) is \(33\)

Answer:

\(\frac{16}{33}\)