What is the probability that he passes the test?

Question

A short multiple choice test has four questions. Each question has five choices, exactly one of which is right. Willie Passitt has not studied for the test, so he guesses answers at random. What is the probability that he passes the test? (A 60 is passing.)

Answer 1

P(guessing a question correctly) = 1/5 = .2

P(guessing wrong) = 4/5 = .8

 

P(at least 3/5 right)

= P(3 right) + P(4 right) + P(5 right)

 

You can now solve using the binomial distribution.

 

P(3 right) = 5C3 * (.2)^3 + (.8)^2

 

P(4 right)= 5C4 * (.2)^4) + (.8)^1

 

P(5 right) = 5C5 * (.2)^5 + (.8)^0