Question

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(ccw), where c denotes a correct answer and w denotes a wrong answer.
p(ccw)=\frac{4}{125} (type an exact answer.)
b. beginning with ccw, make a complete list of the different possible arrangements of two correct answers and one wrong answer, then find the probability for each entry in the list.
p(ccw) - see above
p(cwc)=
p(wcc)=
(type exact answers.)

Explanation:

Step1: Determine probability of correct and wrong answers

The probability of a correct answer $P(C)=\frac{1}{5}$ since there is 1 correct out of 5 options. The probability of a wrong answer $P(W)=\frac{4}{5}$ as there are 4 wrong out of 5 options.

Step2: Calculate $P(CWC)$

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

Step3: Calculate $P(WCC)$

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

Answer:

$P(CWC)=\frac{4}{125}$
$P(WCC)=\frac{4}{125}$