You will take either a basketweaving course or a philosophy

You will take either a basket-weaving course or a philosophy course, depending on what your advisor decides. You estimate that the probability of getting an A in basket weaving is 0.85, while in philosophy it is0.60. However, the chances of your advisor choosing the basket-weaving course is only 10%, while there is an 90% chance that he will put you in the philosophy course. What is the probability that you end up with an A? (Enter your answer to three decimal places.

Solution

By Bayes\' rule,

P(getting A) = P(chose basket)P(got A given basket) + P(chose philo)P(got A given Philo)

P(getting A) = 0.10*0.85 + 0.90*0.60

Thus,

P(getting A) = 0.625 [ANSWER]