**(5 c 3)(.2)**

^{3}(.8)^{2}+ (5 c 4)(.2)^{4}(.8) + .2^{5}**.8**

^{5}+ (5 c 1)(.2)(.8)^{4}+ (5 c 2)(.2)^{2}(.8)^{3}**bold**calculations if you are using a table, but the set-up should match.

assume that random guesses are made for five multiple-choice question on an ACT test, so that there are n=5 trials. each with probability of success (correct) given by p=0.20. use the binomial probability table to find the indicated probability for the number of correct answers.

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James F. | Statistics Graduate Student and TutorStatistics Graduate Student and Tutor

Well, I don't have a binomial probability table (I use a calculator), but the set-up is like this:

P(X is at least 3) = P(X>=3) = P(X=3) + P(X=4) + P(X=5) =** (5 c 3)(.2)**^{3}(.8)^{2} + (5 c 4)(.2)^{4}(.8) + .2^{5}

P(X is fewer than 3) = P(X<3) = P(X=0) + P(X=1) + P(X=2) =** .8**^{5} + (5 c 1)(.2)(.8)^{4} + (5 c 2)(.2)^{2}(.8)^{3}

You may not need to know those **bold **calculations if you are using a table, but the set-up should match.

J.T.

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