Find the conditional probability that a driver was involved in a major accident given that he or she either took or did not take the course.
See solution.
Practice makes perfect
We are given data about the number of drivers who took a defensive driving course in a delivery company. Let's take a look at the given contingency table.
Took Course
Did Not Take Course
Totals
No Major Accidents
3
18
21
At least 1 Major Accident
0
4
4
Totals
3
22
25
We want to determine whether the company made a good decision continuing to offer the course. To do so, we will calculate the conditional probability that the driver had at least 1 major accident given that he or she took the course and did not take the course, respectively.
P(had an accident | took course)
The first column of data shows the total number of drivers who took the course, 3. In the second row of this column, we can see that 0 such drivers had at least 1 major accident.
P(accident | course) = 0/3 = 0%
Therefore, none of the drivers who took the course in the company were involved in a major accident. Similarly, we will calculate the other probability by using the data from the second column.
P(accident | no course) = 4/22 ≈ 18%
Note that about 18 % of the drivers who did not take the course were involved in at least 1 major car accident. Based on the given data and both the probabilities, we can conclude that the course is effective and the company made a good decision.
Extra
Number of Participants
The research conducted by the company may not be reliable enough to decide whether the decision to continue offering the course is good.
Totals
Took Course
3
Did not Take Course
22
Totals
25
Although none of the drivers who took course had a major accident, note that there were only 3 participants of the course compared to 22 remaining drivers. the company should repeat the evaluation with a higher number of participants of the course.
