(t point) Suppose i give you a ist of 21 problems to study, from which I will an

Question

(t point) Suppose i give you a ist of 21 problems to study, from which I will andomly pick 10 questions for your first midterm exam. orran pareorthe midem ouam by competng vou do not know how to solve. Part (a) What is the probability that you completely sove 8 of the 10 questions appearing on the midterm exam? decimals) Part (b) To pass the and understanding how to solve 11 questions of the 21, so there are 10 questions of th (use four you must correctly solve at least half of the 10 questions. What is the probability of you passing the midterm exam? (use four decimals)

Explanation / Answer

Total 21 question available to be chosen for a test
10 Questions are unprepared
11 questions are prepared

(a)
8 Questions appeared from the list of 11 question which are prepared, this can be done in 11C8 ways

Remaining 2 questions are selected from 10 unprepared questions, this can be done in 10C2 ways

Hence required probability = 11C8*10C2/21C10 = 165*45/352716 = 0.0211

(b)
If one passes the test, this means the selected questions contain 5 or more from the list of 11 prepared questions.

Probability that 5 questions are selected from the list of prepared questions = 11C5*10C5/21C10 = 0.3301
6 questions are selected from the list of prepared questions = 11C6*10C4/21C10 = 0.2751
Similarly, for all values of x we have below table

Hence required proability = summation of all P(X=x) = 0.74006

x 5 6 7 8 9 10 P(X=x) 0.33008 0.27507 0.11227 0.02105 0.00156 0.00003

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