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 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 thatsplits 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.

Identical Twins

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

b.After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. What is the probability that she will have identical twins? That is, find the probability of identical twins given that the twins consist of two boys.

Solution 25BSC

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