Chapter 11.5, Problem 1LC

Solution

To state: The Probability $P\left(\text{passed}|\text{studied}\right)$

. 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 $P\left(\text{passed}|\text{studied}\right)=0.89$ .

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 studied students from the above table is 9.

The total numbers of students who studied and passed are 8.

Then the probability of $P\left(\text{passed}|\text{studied}\right)$ :

  $\begin{array}{c}P\left(\text{passed}|\text{studied}\right)=\frac{\text{number of students who passed}}{\text{number of students who studied}}\\ =\frac{8}{9}\\ =0.89\end{array}$

Therefore, the probability is $P\left(\text{passed}|\text{studied}\right)=0.89$ .