SOLUTION: Suppose that an exam has 10 True or False questions. Suppose that a student who doesn’t study has a 50% chance of answering any given question correctly, while a student who do

This problem is to determine the conditional probability.


If a student did not study the subject, the probability for him to answer 8 of 10 
questions correctly is

    P(did not study) =  =  = 0.043945313

(the standard formula for the binomial distribution).



If a student did study the subject, the probability for him to answer 8 of 10 
questions correctly is

    P(did study) =  =  = 0.301989888

(the standard formula for the binomial distribution).



Thus the probability for a random student to answer 8 of 10 questions is

    P = 0.5*P(did not study) + 0.5*(did study) = 0.5*0.043945313 + 0.5*0.301989888 = 0.1729676.


We use the weights 0.5, because Only half of all students study for the exam.


Therefore, the conditional probability that Alice studied for exam given that she answered correctly 8 questions is

      =  = 0.8730  (rounded).    ANSWER