multiple - choice questions each have five possible answers (a, b, c, d, e), one of which is correct. assume…

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.\na. use the multiplication rule to find p(cww), where c denotes a correct answer and w denotes a wrong answer.\np(cww) = \\frac{16}{125} (type an exact answer.)\nb. beginning with cww, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list.\np(cww) - see above\np(wwc) = \np(wcw) =\n(type exact answers.)

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.\na. use the multiplication rule to find p(cww), where c denotes a correct answer and w denotes a wrong answer.\np(cww) = \\frac{16}{125} (type an exact answer.)\nb. beginning with cww, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list.\np(cww) - see above\np(wwc) = \np(wcw) =\n(type exact answers.)

Answer

Explanation:

Step1: Calculate probability of correct and wrong answers

The probability of a correct answer $P(C)=\frac{1}{5}$, and the probability of a wrong answer $P(W)=\frac{4}{5}$.

Step2: Calculate $P(WWC)$

Using the multiplication - rule for independent events, $P(WWC)=P(W)\times P(W)\times P(C)=\frac{4}{5}\times\frac{4}{5}\times\frac{1}{5}=\frac{16}{125}$.

Step3: Calculate $P(WCW)$

Using the multiplication - rule for independent events, $P(WCW)=P(W)\times P(C)\times P(W)=\frac{4}{5}\times\frac{1}{5}\times\frac{4}{5}=\frac{16}{125}$.

Answer:

P(WWC) = $\frac{16}{125}$ P(WCW) = $\frac{16}{125}$