Questions: 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(WWC), where C denotes a correct answer and W denotes a wrong answer. P(W W C)= (Type an exact answer.)

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(WWC), where C denotes a correct answer and W denotes a wrong answer.
P(W W C)=
(Type an exact answer.)

Transcript text: 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 $\mathrm{P}(\mathrm{WWC}$ ), where C denotes a correct answer and W denotes a wrong answer. \[ P(W W C)= \] $\square$ (Type an exact answer.)

Solution

Solution Steps

Step 1: Identify the Sequence of Guesses

Given a sequence of guesses 'WWC', where 'C' represents a correct guess and 'W' represents a wrong guess. In this sequence, there are 1 correct guesses and 2 wrong guesses.

Step 2: Calculate the Probability for a Correct Guess

The probability of guessing a question correctly is $\frac{1}{5}$, since there is one correct answer out of 5 possible answers.

Step 3: Calculate the Probability for a Wrong Guess

The probability of guessing a question incorrectly is $\frac{4}{5}$, since there are 4 wrong answers out of 5 possible answers.

Step 4: Use the Multiplication Rule

To find the probability of the given sequence 'WWC', we multiply the probabilities of each event in the sequence together. The probability is $\left(\frac{1}{5}\right)^{1} \times \left(\frac{4}{5}\right)^{2}$.