Expert: Paul Klarreich - 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
Questioner:   Joel
Category:  Advanced Math
Private:  No
 
Subject:  Probability and statisitcs
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.
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Hi, Joel,

Try looking at the question this way:

He only needs one more right to get at least a 5.  You want

p(at least one more right), which =

1 - p(not getting one more right),

And p(not getting one more right) =

p(getting all six wrong),  which =

(since they are independent)

p(getting one of the six wrong)^6, which =

(4/5)^6.

Does that do it?