Question

Many couples take advantage of ultrasound exams to determine the sex of their baby before it is born. Some couples prefer not to know beforehand. In any case, ultrasound examination is not always accurate. In one medical group, the probability that a girl is correctly identified is 0.89 (that is, this is the probability that the doctor interprets the ultrasound as showing a girl, given that the baby really is a girl), and the probability that a boy is correctly identified is 0.82. The probability of a baby being a girl is 0.48. Consider the next 1000 births handled by this medical group. What is the probability that the baby is a girl, given that the ultrasound indicates it is a girl?

Answer 1

please follow the tree diagram

Think about the next 1000 births handled by this medical group

• are girls
• are boys

of 480 girls, the number of girls that will be identified correctly =

of 520 boys, the number of boys that will be identified correctly =

Now there is a case where a boy is identified as a girl in an ultrasound, the total number of such case is 520-426.4= 93.6

the probability that the baby is a girl, given that the ultrasound indicates that it is a girl is a conditional probability, which will be equal to =