Question

A Statistics student is taking the probability exam and needs to get at least a 60% to pass. There are two sections on the exam, a T/F portion and a multiple choice portion with 4 possibilities on each problem.

4. If the student randomly guesses on the T/F section, what is the probability that she will score exactly 6 out of ten on this section? What is the probability that she will score at least 6 out of ten?

5. If the student randomly guesses on the multiple choice section of the exam, what is the probability that she will score exactly 6 out of ten? At least 6 out of ten?

6. If the student randomly guesses, what is the probability that she scores at least 4 on the T/F section and at most 5 on the multiple choice section?

7. If the student randomly guesses, what is the probability that she scores at least 4 on the T/F section or at most 5 on the multiple choice section?

8. If the professor requires that the student score at least 6 on each part of the exam to pass, what is the probability that the student will pass the exam if she randomly guesses? (round your answer to 5 decimal places)

Answer 1

4:

Since each question is true and false so probability that answer is correct will be

p = P(correct) = 0.50

Let X is a random variable shows the number of correct answers out of 10. The probability that she will score exactly 6 out of ten on this section is

The probability that she will score at least 6 out of ten is

5:

Since each question is multiple choice with 4 possible choices so probability that answer is correct will be

p = P(correct) = 0.25

Let X is a random variable shows the number of correct answers out of 10. The probability that she will score exactly 6 out of ten on this section is

The probability that she will score at least 6 out of ten is