In 1995, Isaac and Alex were graduate econometrics teaching assistants at the University ofWisconsin. They were interested in the effect of going out for drinks with teaching assistantsthe night before econometrics students took preliminary exams on the probability a studentpasses the preliminary exam (students either pass or fail). They took out 25% of people who attended a small liberal arts college and 10% of people who did not attend a small liberal artscollege. Of those who went drinking, 90% from small liberal arts colleges passed and 80% ofthose not from small liberal arts colleges passed. Of those who did not go drinking, 50% ofthose from small liberal arts colleges passed, 60% of those not from small liberal arts collegespassed.z =1 if went drinking with Alex and Isaac (received treatment 1),=0 if did not go drinking with Alex and Isaac (received treatment 0)x =1 if attended small liberal arts college, 0 otherwisey1=outcome on exam if had received treatment 1 (gone drinking),y0=outcome on exam if had received treatment 0 (not gone drinking),y =indicator equal to 1 if passed the exam, 0 if failed.
(a) Calculate P(Z = 1jX = 1).