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)=square ) (type an exact answer.)

Explanation:

Step1: Find the probability of a correct answer

The probability of getting a correct answer \(P(C)\) is \(\frac{1}{5}\) since there is 1 correct answer out of 5 options.

Step2: Find the probability of a wrong answer

The probability of getting a wrong answer \(P(W)\) is \(\frac{4}{5}\) since there are 4 wrong answers out of 5 options.

Step3: Use the multiplication rule for independent events

Since the guesses for each question are independent events, \(P(CWW)=P(C)\times P(W)\times P(W)\).
Substitute the values: \(P(CWW)=\frac{1}{5}\times\frac{4}{5}\times\frac{4}{5}\)

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Answer:

\(\frac{16}{125}\)