Probability in multiple choice exams

[From: ] [author: ] [Date: 12-05-27] [Hit: ]

25!)) ((1/5)^15 (4/5)^25Sum the 16 terms and subtract them from 1-Let X be the number of answers correct.n = 40p = 0.2, q = 1 - 0.2 = 0.......

or
P(passing) = 1 - ( P(guessing 0 correct) + P(guessing 1 correct) +...+ P(guessing 15 correct) )

I would use the second equation to solve the problem because there are fewer terms to have to deal with. (16 terms vs 25 terms)

P(guessing a single question correctly) = 1/5
P(guessing a single question incorrectly) = 4/5
P(guessing 0 correct) = (4/5)^40
P(guessing 1 correct) = 40 (1/5)(4/5)^39
P(guessing 2 correct) = (40(39) / 2) (1/5)^2 (4/5)^ 38

You have to generate all 16 terms with the last one being
P(guessing 15 correct) = (40! / (15! 25!)) ((1/5)^15 (4/5)^25

Sum the 16 terms and subtract them from 1

-

Let X be the number of answers correct.

n = 40

p = 0.2, q = 1 - 0.2 = 0.8

You approve the exam if your X ≥ 16

Because 40*0.4 = 16

P(X ≥ 16) = 1 - P(X ≤ 15)

Look for a table with n = 40, p = 0.2, x ≤ 15, done!

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