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.
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) + .25
P(X is fewer than 3) = P(X<3) = P(X=0) + P(X=1) + P(X=2) = .85 + (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.