suspose that a student who is about to take a multiple choic

suspose that a student who is about to take a multiple choice test has only learned 40% of the material covered by the exam . thus,there is a 40% chance that she will not know the answer to the question. however, if she does not know the answer to the question , she still has a 20% chance of getting the answer right by guessing. if we choose a question at random from the exam, what is the probability that she will get it right

Solution

suspose that a student who is about to take a multiple choice test has only learned 40% of the material covered by the exam . thus,there is a 40% chance that she will not know the answer to the question. however, if she does not know the answer to the question , she still has a 20% chance of getting the answer right by guessing. if we choose a question at random from the exam, what is the probability that she will get it right

P[know answer) =40%

P[Not know answer) =60%

P[know answer & get it right] =40% x 100% = 40%
P[guess answer & get it right] = 20% x 60% = 12%
P[get it right] = sum of the above = 52%

probability that she will get it right = 0.52