Question

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Preeclampsia. Preeclampsia is a medical condition characterized by high blood pressure and protein in the urine of a pregnant woman. It is a serious condition that can be life-threatening to the mother and child. In the article "Women's Experiences Preeclampsia: Australian Action on Preeclampsia Survey of Wom and Their Confidants" (Journal of Pregnancy,Vol. 2011, Issue 1, Article ID 375653), C. East et al. examined the experiences of 68 women with preeclampsia. The following table provides a frequency distribution of instances of prenatal or infant death for infants of women with preeclampsia.

Suppose that one of these women with preeclampsia is randomly selected. Find the probability that the child of the woman selected

(a) died.

(b). died one week to six months after birth.

(c). lived at least six weeks.

Short answer

Part (a) 0.265.

Part (b) 0.118.

Part (c) 0.765.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Preeclampsia is a medical condition characterized by high blood pressure and protein in the urine of a pregnant woman. It is a serious condition that can be life-threatening to the mother and child. In the article "Women's Experiences Preeclampsia: Australian Action on Preeclampsia Survey of Wom and Their Confidants", C. East et al. examined the experiences of 68 women with preeclampsia.

The following table provides a frequency distribution of instances of prenatal or infant death for infants of women with preeclampsia.

Prenatal/Infant Death	Frequency
Stillborn	9
Death within one week	4
Death One week to six weeks	3
Death Six weeks to six months	1
Death after six months	1
Did not die	50

Part (a) Step 2. Find the probability that the child of the woman selected died.

We know that an event's probability ranges from 0 to 1, and both 0 and 1 are included in it.

The formula for the probability of an event is:

$P\left(E\right)=\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

A total of 68 women were examined with preeclampsia. Therefore, the total number of instances will become 68.

The total instances where a child dies is:

$9+4+3+1+1=18$

Let's call the occurrence 'E' the death of the woman's child.

The probability that the child of the woman selected died is:

$$\begin{gathered} p\left(E\right)=\frac{18}{68} \\ =0.265 \end{gathered}$$

Part (b) Step 1. Find the probability that the child of the woman selected died one week to six months after birth.

The total instances where a child dies one week to six months after birth are:

$4+3+1=8$

Now Let's call the occurrence 'E' the death of the woman's child from week one to six months after birth.

The probability that the child of the woman selected died one week to six months after birth is:

$$\begin{gathered} P\left(E\right)=\frac{8}{68} \\ =0.118 \end{gathered}$$

Part (c) Step 1. Find the probability that the child of the woman selected lived at least six weeks.

The total instances where a child lived at least six weeks are:

$1+1+50=52$

Now Let's call the occurrence 'E' the child that lived at least six weeks.

The probability that the child of the woman selected lived at least six weeks is:

$$\begin{gathered} P\left(E\right)=\frac{52}{68} \\ =0.765 \end{gathered}$$