You are taking a multiple choice test for which you have mastered 70% of the material. Assume this means that you have a 0.7 chance of knowing the answer to a random test question, and that if you don’t know the answer to a question then you randomly select among the four answer choices. Finally, assume that this holds for each question, independent of the others. (a) What is your expected score (as a percent) on the exam? Let p be the probability of getting a random question correct. You likely found p in part (a), but in any case you should assume 0.7 < p < 0.9. In parts (b), (c) and (d) you can just use the letter p for this probability. (b) If the test has 10 questions, what is the probability you score 90% or higher? (Do not simplify the expression you get.) (c) What is the probability you get the first 6 questions on the exam correct? (Again, do not simplify the expression you get.) (d) Suppose you need a 90% to keep your scholarship. Would you rather have a test with 10 or 100 questions? Why? (Your answer only needs to be one sentence long.)

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You are taking a multiple choice test for which you have mastered 70% of the material.

Assume this means that you have a 0.7 chance of knowing the answer to a random test

question, and that if you don’t know the answer to a question then you randomly select

among the four answer choices. Finally, assume that this holds for each question, independent of the others.

(a) What is your expected score (as a percent) on the exam?
Let p be the probability of getting a random question correct. You likely found p in part
(a), but in any case you should assume 0.7 < p < 0.9.
In parts (b), (c) and (d) you can just use the letter p for this probability.
(b) If the test has 10 questions, what is the probability you score 90% or higher? (Do not
simplify the expression you get.)
(c) What is the probability you get the first 6 questions on the exam correct? (Again, do
not simplify the expression you get.)
(d) Suppose you need a 90% to keep your scholarship. Would you rather have a test with
10 or 100 questions? Why? (Your answer only needs to be one sentence long.)

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