# Question on Probability!

• January 5th 2009, 05:07 PM
cnmath16
Question on Probability!
49. 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. If the student randomly guesses the answer to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer correct to two decimal places. out of 4 marks
• January 5th 2009, 05:27 PM
Last_Singularity
Quote:

Originally Posted by cnmath16
49. 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. If the student randomly guesses the answer to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer correct to two decimal places. out of 4 marks

Since the student is certain to get at least 4 of the questions correct, he is getting at least a 4 on the exam, then. Thus, it is equivalent to having a 6 (10 questions - 4 guarantees) question test and asking about the probability of getting 1 or more on the exam.

We observe that the chances of him getting any one question correct is 1/5, or 20% and of course, the chance of him getting it wrong would be 4/5, or 80%. Find the probability that he gets all 6 questions wrong first. By independent, we can simply multiple and get $0.8^6$. So that chance that he gets at least 1 question right is the complement of the previous probability, or $1-0.8^6$.