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) = (type an exact answer.)

Explanation:

Step1: Calculate probability of a correct answer

The probability of getting a correct answer $P(C)$ for a single - multiple - choice question with 5 options is $\frac{1}{5}$ since there is 1 correct option out of 5.

Step2: Calculate probability of a wrong answer

The probability of getting a wrong answer $P(W)$ for a single multiple - choice question is $\frac{4}{5}$ since there are 4 wrong options out of 5.

Step3: Use the multiplication rule for independent events

Since the guesses for each question are independent events, for the sequence $CCW$, we multiply the probabilities of each event. So $P(CCW)=P(C)\times P(C)\times P(W)$.
Substitute $P(C)=\frac{1}{5}$ and $P(W)=\frac{4}{5}$ into the formula: $P(CCW)=\frac{1}{5}\times\frac{1}{5}\times\frac{4}{5}=\frac{4}{125}$.

Answer:

$\frac{4}{125}$