Stanley\'s statistics seminar is graded on a Pass/Fail basis. At the end of the

Question

Stanley's statistics seminar is graded on a Pass/Fail basis. At the end of the semester each student is given the option of taking either a two-question quiz (Final A) or a three-question quiz (Final B). To pass the course, students must answer at least one question correctly on whichever quiz they choose. The professor estimates that a typical student has a 45% chance of correctly answering each of the two questions on Final A and a 30% chance of correctly answering each of the three questions on Final B. Which quiz should Stanley choose? Answer the question two different ways.

Explanation / Answer

Solution:

For Final A, n = 2, P(correct answer) = 0.45

Expected number of correct questions = n*p = 2*0.45 = 0.90

For Final B, n = 3, P(correct answer) = 0.30

Expected number of correct questions = n*p = 3*0.30 = 0.90

For Quiz A and B, expected number of correct questions are same.

So, Stanley can choose any one of the test.

Now, for single number of question, Stanley should choose quiz A, because there is lower risk of failing the first question as compared to the quiz B. Quiz A for first attempt have risk (1 – 0.45) = 0.55 while quiz B for first attempt have risk (1 – 0.30) = 0.70. So, minimizing the risk factor, Stanley should choose quiz A.

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