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(cww), where c denotes a correct answer and w denotes a wrong answer.
p(cww)= (type an exact answer.)

Explanation:

Step1: Calculate probability of correct answer

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

Step2: Calculate probability of wrong answer

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

Step3: Use multiplication rule for independent events

Since the guesses for each question are independent events, for the event CWW, we multiply the probabilities of each individual event. So $P(CWW)=P(C)\times P(W)\times P(W)$.
Substitute $P(C)=\frac{1}{5}$ and $P(W)=\frac{4}{5}$ into the formula: $P(CWW)=\frac{1}{5}\times\frac{4}{5}\times\frac{4}{5}=\frac{16}{125}$.

Answer:

$\frac{16}{125}$