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Elementary Statistics 11th

Identical and Fraternal Twins. 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 Nortbern California Tivin 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, I/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. $$\begin{array}{lcccc} & \multicolumn{3}{c} {\text { Sexes of Twins }} \\& \text { boy/boy } & \text { boy/girl } & \text { girl/boy } & \text { girl/gin } \\\hline \text { Identical Twins } & 5 & 0 & 0 & 5 \\\text { Fraternal Twins } & 5 & 5 & 5 & 5\end{array}$$

Fraternal Twins If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will have one child of each sex?