(3) A student received an \"A\" on the first test of the semester. The student w

Question

(3) A student received an "A" on the first test of the semester. The student wants to calculate the probability of scoring an "A" on the second test. Historically, the instructor knows that the joint probability of scoring "A "s on the first two tests is 0.5. Also, historically, the probability that a student scores an "A" on the second test given that a student scored an "A" on the first test is 0.9. What is the probability that a student will score an "A" on the first test? (10 points) . (4) Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective? (10 points) (5) Ten students are being interviewed for a class office. Six of them are female and four are male. Their names are all placed in a box and two students are selected for the interviews. (10 points) c. What is the probability that both of those selected are female? d. What is the probability that at least one is male?

Explanation / Answer

Question 4:

Here we are given that:

Probability of getting an A on both the first two tests is given as: 0.5,

Therefore, P(A on test 1 and test 2 ) = 0.5

Also, given that there is an A in first test, probability of getting an A in second test would be given as:

P( A in second test | A in first test ) = 0.9

Using Bayes theorem, we get:

P( A in first test ) = P(A on test 1 and test 2 ) / P( A in second test | A in first test )

P( A in first test ) = 0.5 / 0.9

P( A in first test ) = 0.5556

Therefore 0.5556 is the required probability here.

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