Expert: Steve Holleran - 5/12/2008

Question
On a multiple-choice test of 10 questions, each question has 5 possible answers. A student is certain of the answers to 4 questions but is totally baffled by 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer to two decimal places.

Answer
Hi Joel,

Okay, prob/stat is not my best field, but I think I've got something here.

 To get a 5 or more, if the student knows 4 of them cold, he only has to answer 1 of the remaining 6 correctly.  So, all we have to find is the probability that he will get at least 1 of the 6 correct.  An easy way to do this is to think like this:

 P(at least 1 correct) = 1 - P(none correct)

Since each question has 5 choices, each question carries a probability of 1/5 to get it correct, and 4/5 to get it incorrect.

We want 1 - P(all wrong), so that would be :

                       1 - (4/5)^6  

because you want to calculate the number of ways to get all 6 wrong (only 1 way) and you want to multiply the probabilities of getting each individual question wrong.

I calculate this tto be 1 - .262144 = 0.7379, or 0.74 to two places.


Hope this is okay.
Steve