A study was conducted among a certain group of union members whose health insurance policies required second opinions prior to surgery. Of those members whose doctors advised them to have surgery, 20% were informed by a second doctor that no surgery was needed. Of these, 70% took the second doctor's opinion and did not go through with the surgery. Of the members who were advised to have surgery by both doctors, 95% went through with the surgery. What is the probability that a union member who had surgery was advised to do so by a second doctor?
A) 0.5
B) 0.93
C) 0.15
D) 0.81

Question

Quizplus · Accepted Answer

The probability that a union member who had surgery was advised to do so by a second doctor is calculated by considering the two groups: those advised against surgery by the second doctor but went through with it anyway, and those advised to have surgery by both doctors. Since 95% of those advised by both doctors went through with the surgery and only a small fraction of those advised against it by the second doctor proceeded, the majority of surgeries were performed with the endorsement of both doctors, leading to a high probability, in this case, 0.93.

A Study Was Conducted Among a Certain Group of Union