Seventy students have registered their intention to participate in the behaviour

Question

Seventy students have registered their intention to participate in the behavioural economics course. For each of the five problem sets forty-eight students will be selected at random to have their work graded, the random draws will be independent.

(a) Calculate the probability that a particular student will not be selected for any of the five problem sets.

(b) Calculate the probability that a particular student will be graded for exactly one of the five problem sets.

(c) A student is not selected to be graded for the first problem set, calculate the probability that the student is not graded for any problem set conditional on this event.

(d) A student decides to hand in three of the five problem sets, calculate the probability that the student was selected to be graded for the two problem sets that were not handed in and not for the three that were.

Explanation / Answer

Total registered students = 70

Here p^ (if any registered student is selected for be selected at random) = 48/70 = 0.6857

(a) here n = 5 and p = 0.6857

and x is the number of sets any particular student will be get selected.

Pr(x = 0) = BIN ( x= 0 ; 5 ; 0.6857) = 5C0 * (0.6857)0 (1 - 0.6857)5 = 0.0031

(b) Pr(x = 1) = BIN (x = 1 ; 5 ; 0.6857) =  5C1 * (0.6857)1 (1 - 0.6857)4 = 0.0335

(c) As random draw are indpendent then if a student is not selected for the first problem set, we not affect the probability that the student is not graded for any problem set conditional on this event.

so,

Pr(A students is not graded in next 4 sets l students is not graded on first set) = (1 - 0.6857)5/ (1 - 0.6857) = 0.0098

(d) Here Pr(Student was selected to be graded for the problem sets that were not handed in and not for the three that were) = 3C3 (1 - 0.6857)32C2 (0.6857)2 = 0.0146

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