Question

An irregular student is taking two courses microeconomics and econometrics. Probability that she passes microeconomics exam is 0.70; econometrics 0.65 and both of the courses is 0.55.

1. Find the probability that she passes microeconomics or econometrics exams.
2. Find the probability that she fails both of the exams.

If she passed microeconomics exam what is the probability that she passes econometrics exam?

Answer 1

Let ME : she pass a microeconomics exam

EM : she passed a econometrics exam

Given P( ME) = 0.70, P( EM) = 0.65 , P( ME EM) = 0.55

a) P( ME U EM) = P( ME) + P(EM) - P( ME EM)

P( ME U EM) = 0.70+0.65-0.55 = 0.80

b) P ( ME​​​​​c​U EM​​​​​c​) = P ( ME EM)c = 1 - P( ME EM)

P( ME​​​​​C​U EM​​​​​C​) = 1 - 0.55 = 0.45

c) P( EM/ME) = P( ME EM)/P(ME) = 0.55/0.70

P( EM/ME) = 0.7857