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28 August, 10:32

A student takes a true-false test that has 12 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (10 or more)

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  1. 28 August, 12:26
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    Step-by-step answer:

    assuming the true-false test have equal probabilities (each 0.5), we can use the binomial probability to calculate the sum of probabilities of getting 10, 11 or 12 questions correctly out of 12.

    p=probability of success = 0.5

    N=number of questions

    x = number of correct answers

    then

    P (x) = C (N, x) (p^x) ((1-p) ^ (N-x))

    where C (N, x) = N! / (x! (N-x) !) = number of combinations of taking x objects out of N.

    P (10) = C (12,10) (0.5^10) ((1-0.5) ^2) = 33/2048 = 0.01611

    P (11) = C (12,11) (0.5^11) ((1-0.5) ^1) = 3/1024 = 0.00293

    P (12) = C (12,12) (0.5^12) ((1-0.5) ^0) = 1/4096 = 0.00024

    for a total probability of 79/4096 = 0.01929
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