# Identical and Fraternal Twins. In Exercises 2528, use the

Chapter 4, Problem 26

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QUESTION:

Identical and Fraternal Twins. In Exercise, use the data in the following table. Instead of summarizing observed results, the entries reflect the actual probabilities based on births of twins (based on data from the Northern California Twin Registry and the article “Bayesians, Frequentists, and Scientists” by Bradley Efron, Journal of the American Statistical Association, Vol. 100, No. 469). Identical twins come from a single egg that splits into two embryos, and fraternal twins are from separate fertilized eggs. The table entries reflect the principle that among sets of twins, 1/3 are identical and 2/3 are fraternal. Also, identical twins must be of the same sex and the sexes are equally likely (approximately), and sexes of fraternal twins are equally likely.

$$\begin{array}{l} \text { Sexes of Twins }\\ \begin{array}{l|c|c|c|c} \hline & \text { boy } / \text { boy } & \text { boy } / \text { girl } & \text { girl } / \text { boy } & \text { girl } / \text { girl } \\ \hline \text { Identical Twins } & 5 & 0 & 0 & 5 \\ \hline \text { Fraternal Twins } & 5 & 5 & 5 & 5 \\ \hline \end{array} \end{array}$$

a. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have fraternal twins?

b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twins consisting of one boy and one girl. What is the probability that she will have fraternal twins?

QUESTION:

Identical and Fraternal Twins. In Exercise, use the data in the following table. Instead of summarizing observed results, the entries reflect the actual probabilities based on births of twins (based on data from the Northern California Twin Registry and the article “Bayesians, Frequentists, and Scientists” by Bradley Efron, Journal of the American Statistical Association, Vol. 100, No. 469). Identical twins come from a single egg that splits into two embryos, and fraternal twins are from separate fertilized eggs. The table entries reflect the principle that among sets of twins, 1/3 are identical and 2/3 are fraternal. Also, identical twins must be of the same sex and the sexes are equally likely (approximately), and sexes of fraternal twins are equally likely.

$$\begin{array}{l} \text { Sexes of Twins }\\ \begin{array}{l|c|c|c|c} \hline & \text { boy } / \text { boy } & \text { boy } / \text { girl } & \text { girl } / \text { boy } & \text { girl } / \text { girl } \\ \hline \text { Identical Twins } & 5 & 0 & 0 & 5 \\ \hline \text { Fraternal Twins } & 5 & 5 & 5 & 5 \\ \hline \end{array} \end{array}$$

a. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have fraternal twins?

b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twins consisting of one boy and one girl. What is the probability that she will have fraternal twins?

Step 1 of 3

The data on the birth of identical twins and fraternal twins with respect to their gender has been given.