Chapter 11.5, Problem 11PPSE

Solution

a.

To state: The probability that a nursing student passed the board exams given that he or she took the preparatory class. The table below shows the number of nursing students who took preparatory class before taking their board exams:

	Preparatory Class	No Preparatory Class	Totals
Passed Exams	14	11	25
Did not Pass Exams	3	6	9
Totals	17	17	34

The resultant probability is $P\left(\text{passed}|\text{Preparatory class}\right)\approx 0.82$ .

Given information:

The given table is:

	Preparatory Class	No Preparatory Class	Totals
Passed Exams	14	11	25
Did not Pass Exams	3	6	9
Totals	17	17	34

Explanation:

Consider the given table:

	Preparatory Class	No Preparatory Class	Totals
Passed Exams	14	11	25
Did not Pass Exams	3	6	9
Totals	17	17	34

The total number of students who took preparatory class is 17.

The total numbers of students who took preparatory class and passed are 14.

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

  $\begin{array}{c}P\left(\text{passed}|\text{Preparatory class}\right)=\frac{\text{number of students who passed}}{\text{number of students who took preparatory class}}\\ =\frac{14}{17}\\ \approx 0.82\end{array}$

Therefore, the probability is $P\left(\text{passed}|\text{Preparatory class}\right)\approx 0.82$ .

b.

To state: The probability that a nursing student did not pass the board exams given that he or she did not take the preparatory class.

The resultant probability is $P\left(\text{Did not passed}|\text{No Preparatory class}\right)\approx 035$ .

Given information:

The given table is:

	Preparatory Class	No Preparatory Class	Totals
Passed Exams	14	11	25
Did not Pass Exams	3	6	9
Totals	17	17	34

Explanation:

Consider the given table:

	Preparatory Class	No Preparatory Class	Totals
Passed Exams	14	11	25
Did not Pass Exams	3	6	9
Totals	17	17	34

The total number of students who did not take preparatory class is 17.

The total numbers of students who did not take the preparatory class and not passed are 6.

Then the probability of $P\left(\text{Did not passed}|\text{No Preparatory class}\right)$:

  $\begin{array}{c}P\left(\text{Did not passed}|\text{No Preparatory class}\right)=\frac{\text{students who did not passed}}{\text{students who did not took preparatory class}}\\ =\frac{6}{17}\\ \approx 0.35\end{array}$

Therefore, the probability is $P\left(\text{Did not passed}|\text{No Preparatory class}\right)\approx 035$ .

c.

To identify: Whether it is a good decision if a student takes the preparatory class before he takes the board exams.

Yes, it is a good decision if a student takes the preparatory class before he takes the board exams.

Given information:

The given statement says that whether it is a good decision if a student takes the preparatory class before he takes the board exams.

Explanation:

From part (a) and part (b):

The probability of passed exam by students who took the preparatory class is: $\frac{14}{17}$

The probability of passed exam by students who did not take the preparatory class is: $\frac{11}{17}$

The probability $\frac{14}{17}$ is greater than $\frac{11}{17}$ .

Therefore, to take preparatory class before board exams is a good decision.