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1) There are 168 students currently registered in CPS420. This final exam is graded out of...

1) There are 168 students currently registered in CPS420. This final exam is graded out of 80. For the purposes of this question you can assume that all the marks are integers.

a) What is the least number of final exams that will need to be graded to guarantee that at least 2 students in this class have the same grade in this final exam? Explain your answer.

b) You want to make a bet that there will be a group of at least x CPS420 students who will all have the same grade on this exam. How large can you make x and still be guaranteed to win your bet? Explain your answer.

Math   Statistics-And-Probability   
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Answer #1

a) Atleast 82 final exam will be need to be graded to guarantee that atleast 2 students in this class will have the same grade in the final exam. This is because there are 168 students and the students can get a grade from 0 to 80. So there are 81 possible grades that can be obtained without any 2 people getting the same grade. So, only 82 exam needs to graded in order to guarantee that atleast 2 students have the same grade in the final exam.

b) We can safely bet that there will be a group of atleast 3 students that will receive the same grades. This is because as there are 168 students and 81 possible grades ranging from 0 to 80.

168/81 = 2.07 > 2, hence we can say that there will be a group of atleast 3 CPS420 students who will all have the same grade.

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