Question

The two-way frequency table below shows how many students passed their driving test aswell as the number who took a preparatory class. Find the probability that a student passedthe test, given that he or she took the class.PassedClass42Failed1810No class110710O 5381O 310O 1427None of the other answers are correct

Answer 1

Problem

Solution

For this problem we can define the following events:

A= The student passed the test

B= The student took the class

From the table given we can calculate the following probabilities:

P(A)= (42+11)/81=53/81

P(B)= (42+18)/81= 60/81

P(A and B)= 42/81

We want to find the following probability:

P(A|B) = P(A and B)/P(B)

And replacing we got:

P(A|B)= 42/81 /(60/81)= 42/60

And if we simplify we got:

P(A|B)= 21/30= 7/10