On a true-false test, each question has exactly one correct answer: true, or false. A student knows the correct answer to 70% of the questions on the test. Each of the remaining answers she guesses at random, independently of all other answers. After the test has been graded, one of the questions is picked at random. Given that she got the answer right, what is the chance that she knew the answer?

My first try was 0.70 * 1 + 0.3 * 1/2 = 85/100. But this is not correct. Could someone help me out ?

Thank you!

Question

On a true-false test, each question has exactly one correct answer: true, or false. A student knows the correct answer to 70% of the questions on the test. Each of the remaining answers she guesses at random, independently of all other answers. After the test has been graded, one of the questions is picked at random. Given that she got the answer right, what is the chance that she knew the answer?

My first try was 0.70 * 1 + 0.3 * 1/2 = 85/100. But this is not correct. Could someone help me out ? 

Thank you!

agent0smith · Answer

In case the last link wasn't working correctly, http://openstudy.com/study#/updates/517e3410e4b007218446c5d5

anonymous · Answer

@agent0smith, I understand that the chance that she got the answer right is 0.85%, but given that she got the answer right, what is the chance that she knew the answer? I thought it's 0.7, but I was wrong. Could you help with this, please?

agent0smith · Answer

Its in the above link @njux

agent0smith · Answer

You still need to put the numbers i gave into the formula...

anonymous · Answer

Well, then I obviously don't get what in this case is A and what is B?

agent0smith · Answer

I didnt use A and B, i used K and R... i stated what they both are in the other question

anonymous · Answer

So this means that P (K|R) = P(R|K)*P(K)/P(R)?

agent0smith · Answer

Yep

anonymous · Answer

Thank you very much, everything is clear :)

anonymous · Answer

@agent0smith thanks a lot!