A student is thinking a multiple choice exam in which each e

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?

Solution

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