"5. Multiple-choice questions each have five possible answers (a, b,c, d,e), one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find P(WCC), where C denotes a correct answer and W denotes a wrong answer. b. Beginning with WCC, make a complete list of the different possible arrangements of two correct answers and one wrong answer and find the probability of each. c. Based on the results of part (b) what is the probability of getting exactly two correct answers when three guesses are made?"

A) P(WWC) = 0.128

B) P(WCC) = 0.032

P(CWC) = 0.032

P(CCW) = 0.032

C) probability of getting 2 correct answers when 3 guesses are made is i.e P (1 wrong and 2 correct) = 0.064

Step-by-step explanation:

A) Using the multiplication rule, we have; P(A and B) = P(A) x P(B)

Probability of a wrong answer = 4/5 = 0.8

Probability of a correct answer = 1/5 =0.2

Thus; P(WWC) = 0.8 x 0.8 x 0.2 = 0.128

B) Beginning with one wrong and two correct answers, a complete list of all possibilities is;

P(WCC), P(CWC), P(CCW)

Hence the complete list is;

(0.8 x 0.2 x 0.2); (0.2 x 0.8 x 0.2); (0.2 x 0.2 x 0.8)

So we have;

P(WCC) = 0.032

P(CWC) = 0.032

P(CCW) = 0.032

C) Based on the results above, the probability of getting 2 correct answers when 3 guesses are made is i.e P(1 wrong and 2 correct) = 2 x 0.032 = 0.064

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