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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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

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

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

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

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