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
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