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pakinam
 2 years 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?
pakinam
 2 years 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?

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

reemii
 2 years ago
Best ResponseYou've already chosen the best response.2for 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.

reemii
 2 years ago
Best ResponseYou've already chosen the best response.2now i think you can replace all quantities in the fraction. right?

sarah10
 2 years ago
Best ResponseYou've already chosen the best response.0@reemii can you help me out in this question how to solve it

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.0@reemii doesn't that give a probability greater than 1...?

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

annacn1024
 2 years ago
Best ResponseYou've already chosen the best response.0Sounds 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.
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