Chapter 11.5, Problem 2LC

Solution

To state: The Probability $P\left(\text{did not study}|\text{failed}\right)$

. The contingency table is shown below:

	Passed	Failed	Totals
Studied	8	1	9
Did not Study	3	6	9
Totals	11	7	18

The resultant answer is $P\left(\text{did not study}|\text{failed}\right)=0.86$ .

Given information:

The given table is:

	Passed	Failed	Totals
Studied	8	1	9
Did not Study	3	6	9
Totals	11	7	18

Explanation:

Consider the give table:

	Passed	Failed	Totals
Studied	8	1	9
Did not Study	3	6	9
Totals	11	7	18

The total number of failed students from the above table is 7.

The total numbers of students who did not studied and failed are 6.

Then the probability of $P\left(\text{did not study}|\text{failed}\right)$ :

  $\begin{array}{c}P\left(\text{did not study}|\text{failed}\right)=\frac{\text{number of students who did not study}}{\text{number of students who failed}}\\ =\frac{6}{7}\\ =0.86\end{array}$

Therefore, the probability is $P\left(\text{did not study}|\text{failed}\right)=0.86$ .