Question

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 0.90, while in philosophy it is 0.60. However, the chances of your advisor choosing the basket-weaving course is only 20%, while there is an 80% 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.)

Answer 1

Answer: 0.660

Step-by-step explanation:

Denote $B, P$ as the event that you will be put in the basket-weaving course and the event that you will be put in the philosophy course, respectively. Denote $A, X$ as the event that you will get an A and the event that you will not get an A, respectively.

Using the addition rule and the multiplication rule:

$P(A) = P(A \cap B) + P(A \cap P) = P(B) \times P(A|B) + P(P) \times P(A|P)\\ = 20\% \times 0.90 + 80\% \times 0.60 = 0.660$