You are in college and picked a couple of classes for this s

You are in college and picked a couple of classes for this semester. You wonder which classes you should drop, if any. 25% of classes suck and should be dropped. If a class sucks, the professor is kind of an idiot 70% of the time. Regardless of whether their classes suck or not, 20% of professors are kind of idiots. You are in a class and observe that the professor is kind of an idiot. What is the posterior probability that the class is going to suck (and ought to be dropped)? A. 0.66 B. 0.77 C. 1 D. 0.88 E. 0.5

Solution

Let

I = professor is idiot
S = class sucks

Thus,

P(S|I) = P(S) P(I|S) / P(I)

= 0.25*0.70 / 0.20

= 0.875 = 0.88 [ANSWER, OPTION D]