Multiple-choice questions each have five possible answers left parenthesis a comma b comma c comma d comma e right parenthesis​, 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(WWC​)equals
nothing ​(Type an exact​ answer.)
b. Beginning with WWC​, 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(WWC​)minussee above
​P(WCW​)equals
​P(CWW​)equals ​(Type exact​ answers.)
c. Based on the preceding​ results, what is the probability of getting exactly one correct answer when three guesses are​ made?
nothing ​(Type an exact​ answer.)

1 answer

a. To find P(WWC), we use the multiplication rule. There is a 4/5 chance of getting the first question wrong, a 4/5 chance of getting the second question wrong, and a 1/5 chance of getting the third question correct. Multiply these probabilities together:

P(WWC) = (4/5) * (4/5) * (1/5) = 16/125

b. There are three different possible arrangements of one correct answer and two wrong answers: WWC, WCW, and CWW. We have already found P(WWC) in part (a). Now we need to find P(WCW) and P(CWW):

P(WCW) = (4/5) * (1/5) * (4/5) = 16/125

P(CWW) = (1/5) * (4/5) * (4/5) = 16/125

c. To find the probability of getting exactly one correct answer when three guesses are made, sum up the probabilities found in part (b):

P(Exactly one correct answer) = P(WWC) + P(WCW) + P(CWW) = 16/125 + 16/125 + 16/125 = 48/125