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?

Answer 1

wht is the last condition that u drawn...

Answer 2

Not sure which one you mean...? The 1 is because she gets 100% of the questions she knows correct. The rest she guesses and has a 50% chance of being right.

Let's make event K her knowing the right answer, and event R getting the question right. We need to find P(K|R):

\[\Large P(K|R) = \frac{ P(R|K) \times P(K) }{ P(R) }\]

Answer 3

whts p(r)

Answer 4

R is the event that she gets the answer Right.
K is the event she Knows the answer.

P(R|K) = 1
P(K) = 0.7
P(R) = P(R|K)+P(R|K') = 0.7 + 0.15 = 0.85

P(R|K) means she gets the answer right, given she knew the answer. P(R|K') means she gets the answer right, but did not know the answer.

Now we can put those numbers into that formula above... it all comes from here btw: http://upload.wikimedia.org/wikipedia/commons/1/18/Bayes%27_Theorem_MMB_01.jpg and http://upload.wikimedia.org/wikipedia/commons/6/61/Bayes_theorem_tree_diagrams.svg

Answer 5

ok....thanx a lot...u r a real genius..

Answer 6

lol thanks, I hope you were able to follow it all :)

Answer 7

yup..i did understud..:)

Answer 8

what is an exact answear
I understand nothing

Answer 9

If you read it all carefully from start to finish, you should understand it, assuming you understand a little bit about probability and the symbols.