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On a truefalse 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?
 11 months ago
 11 months ago
On a truefalse 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?
 11 months ago
 11 months ago

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reemiiBest ResponseYou've already chosen the best response.2
\(P(\text{she knewshe got it right})=\frac{P(\text{got rightknew})}{P(\text{got rightknew})P(\text{knew})+P(\text{got rightdidn't know})P(\text{didn't know})}\)
 11 months ago

reemiiBest ResponseYou've already chosen the best response.2
for example, you know that the numerator is 1 for example you know that P(got it rightdidn't know) is due to luck (like coin tossing..), it involves a 1/2 probability in here.
 11 months ago

reemiiBest ResponseYou've already chosen the best response.2
now i think you can replace all quantities in the fraction. right?
 11 months ago

sarah10Best ResponseYou've already chosen the best response.0
@reemii can you help me out in this question how to solve it
 11 months ago

agent0smithBest ResponseYou've already chosen the best response.0
@reemii doesn't that give a probability greater than 1...?
 11 months ago

reemiiBest ResponseYou've already chosen the best response.2
i forgot the factor P(she knew) in the numerator. then it's correct.
 11 months ago

annacn1024Best ResponseYou've already chosen the best response.0
Sounds like 14 times out of twenty she knows the answer 3 times out of twenty she guesses correctly 3 times out of twenty she does not. 14/17 she knew the answer.
 11 months ago
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