Need Help With Binomial Distribution Please?

Could you please explain how to solve this ? (Just an explanation instead of an answer would be great).
thanks in advance
A student is taking a multiple choice test and is able to discount 2/5 of the possible answers. But he has to guess between the remaining options. The test has 20 questions. Find the probability that he gets less than 4 correct.
(b) Another student doing the same test has done enough work to know the correct answers to half of the questions. In each of the other questions he can rule out 3/5 of the given answers but then has to guess the rest.
Find the probability that he scores more than 17 marks. Also find the probability that he gets no more than 1 question wrong.

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One Response to “Need Help With Binomial Distribution Please?”

  1. Pi R Squared says:

    Hi,
    A student is taking a multiple choice test and is able to discount 2/5 of the possible answers. But he has to guess between the remaining options. The test has 20 questions. Find the probability that he gets less than 4 correct.
    20nCrX(3/5)^(x)(2/5)^(20 – x) if x = 0,1,2, or 3
    1 x 10^-8
    3.3 x 10^-7
    4.7 x 10^-6
    4.2 x 10^-5
    Total 4.7 x 10^-5, virtually zero
    (b) Another student doing the same test has done enough work to know the correct answers to half of the questions. In each of the other questions he can rule out 3/5 of the given answers but then has to guess the rest.
    Find the probability that he scores more than 17 marks.
    1.06 + .158 + .0001 = 1.12% <==ANSWER Also find the probability that he gets no more than 1 question wrong. .158 + .0001 = .1581% <==ANSWER I hope that helps!! 🙂

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