Students in a class are given a study guide of 20 questions ofwhich 10 will be p

Question

Students in a class are given a study guide of 20 questions ofwhich 10 will be part of the upcoming exam. A given student knowshow to solve 15 out of the 20 questions of the study guide. What isthe probability that a given student will get all of the 10questions correct? What is the probability that a given studentwill get 8 questions correct?

The answer to the first part is 21/1929. However, I do not know howthe answer was obtained. I am a tutor and was stuck on this problemearlier today during a tutoring session.

Thank you very much for your help.

Explanation / Answer

We have to assume that the questions are chosen through simplerandom selection.  Having done so, we can find theprobability of meeting a given condition by taking the number ofpossible combinations meeting the condition and dividing by thetotal number of combinations possible. . The total number possible is 20choose10, or 20!/(10!10!),which is a big number. STATA tells me that that's 184756. . The total number of combinations where the student knows all10 requires us to pick 10 questions from the student's 15, or15!/(10!5!) = 15*14*13*12*11*10!/(5*4*3*2*10!) = 3*7*13*11=3003. . 3003/184756 =21/1292. . Hmh, either I've screwed up, or there's a typo in youranswer.

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