6.73 Radiologists are often asked to predict the gender of a baby from ultrasound images made during pregnancy.

The authors of the paper “The Use of Three-

Dimensional Ultrasound for Fetal Gender Determination in the First Trimester” (The British Journal of Radiology,

[2003]: 448–451) followed up on 159 predictions made by a particular radiologist (Radiologist 1) to determine whether or not they were correct. Data from the paper is summarized in the accompanying table.

Radiologist 1 Predicted Male Predicted Female Baby Is Male 74 12 Baby Is Female 14 59

a. Assuming that these data are representative of gender predictions made by Radiologist 1, estimate the probability that a gender prediction is correct, given that the baby is male.

b. Assuming that these data are representative of gender predictions made by Radiologist 1, estimate the probability that a gender prediction is correct, given that the baby is female.

c. For Radiologist 1, is a gender prediction more likely to be correct if the baby is male? Explain.

d. Estimate the probability that a gender prediction made by Radiologist 1 is correct.