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 0.90, 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.

Solution

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Given

Probability of getting A in basket weaving = 0.9

Probability of getting A in philosophy = 0.6

Probability of advisor choosing basket weaving = 0.2

Probability of advisor chosing philosophy = 0.8

Hence Probability of ending up with an A is

0.2*0.9 + 0.6*0.8

= 0.18 + 0.48

= 0.66

Solution