Dr. Palpatine teaches statistics at Coruscant University. Hebelieves there are three types of classes he may encounter:
(P) Poor classes, where only 70% of the students will be able topass exam 1 in the course.
(A) Average classes, where 85% of the students will be able topass exam 1.
(G) Good classes, where 95% of the students will be able to passexam 1.
Assuming Palpatine teaches a class of 35 students...
If the class is poor (P), what is the probability that exactly30 of them will pass (E), that is what is P(E|P)? _______
If the class is average (A), what is the probability thatexactly 30 of them will pass (E), that is what is P(E|A)?_______
If the class is average (G), what is the probability thatexactly 30 of them will pass (E), that is what is P(E|G)?_______
Now suppose that Palpatine initially believed the probabilitythat his class was poor, average, and good was 25%, 50%, and 25%respectively. Use Bayes' Rule and the results above to find P(G|E),the probability his class is a good one (G) given the evidence Ethat exactly 30 of them passed the first exam. ______
