A student is thinking a multiple choice exam in which each equation has 5 possib
ID: 3380769 • Letter: A
Question
A student is thinking a multiple choice exam in which each equation has 5 possible answers, exactly one of which is a correct. If the student knows the answer he selects the correct answer. Otherwise he selects one answer at random from the 5 possible answers. Suppose that the student knows the answer to 70% of the questions.
(1) What is the probability that on a given question the student gets the correct answer?
(2) If the student gets the correct answer to the question, what is the probability that he knows the answer?
Explanation / Answer
Sol)
a) We know P(know the answer)=0.7
P(know the answer)=0.7.
On a question chosen at random, he either knows the answer or he doesn't. If he does, then
P(answer correctly / know correct answer)=1P(answer correctly|know correct answer)=1.
If he doesn't, then P(answer correctly|doesn't know correct answer)=0.7(0.3)4 =0.00567
B)
Probability that she guessed the answer and got it correct = 30%*0.5 = 0.15
Out of this I'm only concerned with the probability that she knew the answer.
whose prabability is = 0.7
So probability that she knew the answer, given that she got it right = 0.7/(0.7 + 0.15) =0.8235
= 14/17
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