A student takes a 20 question multiple choice exam where ear

A student takes a 20 question multiple choice exam where earch question has 5 possible choices. Passing is 60%. Suppose the student guesses on every question. FInd these probablities:

A) getting exactly 3 questions right.

B) getting at most three questions correct

C) Passing the exam.

D) getting a B (80%) on the exam.

Solution

No of questions -- 20

No of choices -- 5

p = selecting a right choice = 1/5 = 0.2

X - no of questions rightly answered follow a Binomial with p = 0.2 and n = 20

a) P(x=3) = 20C3(0.2)³(0.8)⁷ = 0.2053

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b) P(X<=3) = P(x =0, 1, 2 or 3) = 0.4114

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c) P(passing the exam) = P(getting >60%)

= P(x>=12) = 0.0001

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d) P(getting 80%) = P(X=16)

= 1.3005x10^-8