Please see the attached file.

Probability
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A test consists of multiple-choice questions, each having four possible answers (a,b,c,d) one of which is correct. Assuming that you guess the answers to six such questions.

a.) Use the multiplication rule to find the probability that the first two guesses are wrong and the last four guesses are correct. That is, find P(WWCCCC), where C denotes a correct answer and W denotes a wrong answer.

b.) Beginning with WWCCCC, make a complete list of the different possible arrangements of two wrong answers and four correct answers, then find the probability for each entry in the list.

Answer

Since there are four possible answers, the probability that the selected one is correct is P(C) = ¼ and probability of selecting a wrong answer is P(W) = ¾

a) P(WWCCCC) =P(W).P(W).P(C) P(C) P(C) P(C)
= ¾*3/4*1/4*1/4*1/4*1/4
= 9/4096

b) Complete list of possible arrangements
Event Probability
{W,W,C,C,C,C} 9/4096
{W,C,W,C,C,C} 9/4096
{W,C,C,W,C,C} 9/4096
{W,C,C,C,W,C} 9/4096
{W,C,C,C,C,W} 9/4096
{C,W,W,C,C,C} 9/4096
{C,W,C,W,C,C} 9/4096
{C,W,C,C,W,C} 9/4096
{C,W,C,C,C,W} 9/4096
{C,C,W,W,C,C} 9/4096
{C,C,W,C,W,C} 9/4096
{C,C,W,C,C,W} 9/4096
{C,C,C,W,W,C} 9/4096
{C,C,C,W,C,W} 9/4096
{C,C,C,C,W,W} 9/4096