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)=\frac{16}{125} ) (type an exact answer.)
b. beginning with ( cww ), make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list.
( p(cww) )-see above
( p(wwc)=\frac{16}{125} )
( p(wcw)=\frac{16}{125} )
(type exact answers.)
c. based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

(ty an exact answer.)

Explanation:

Step1: Analyze the number of arrangements

We have three arrangements: CWW, WWC, WCW. Each has the same probability.

Step2: Calculate the total probability

Since each arrangement has a probability of \(\frac{16}{125}\), and there are 3 such arrangements.
We use the formula \(P=\sum_{i = 1}^{n}P_i\). Here \(n = 3\) and \(P_i=\frac{16}{125}\) for \(i=1,2,3\)
So \(P=\frac{16}{125}+\frac{16}{125}+\frac{16}{125}\)

$$
LATEXBLOCK0
$$

Answer:

\(\frac{48}{125}\)