1)A quiz consists of 8 multiple choice questions, each with 5 possible answers.

Question

If random guesses are made for all 8 questions, find the probability that a
student will answer exactly 5 correctly.

A. 0.999 B. 0.009 C. 0.990
D. There is not enough information to answer this question.
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d. If random guesses are made for all 8 questions, find the probability that a
student will answer less than 4 correctly.
A. 0.944 B. 0.375 C. 0.046

D. There is not enough information to answer this question.

Answer 1

For each question, prob(correct) = 1/5
prob(wrong) = 4/5

to have exactly 5 of the 8 correct
= C(8,5) (1/5)^5 (4/5)^3
= ....

b) prob(none correct) + prob(1 correct) + prob(2 correct) + prob(3 correct)
= C(8,0) (1/5)^0 (4/5)^8 + C(8,1) (1/5)^1 (4/5)^7 + ...
= appr .16777 + .33554 + ....
= ....