Use the multiplication rule to find the probability that the first three guesses are wrong and the fourth is correct.

Question

Multiple-choice questions each have 5 possible answers, one of which is correct. Assume that you guess the answers to 4 such questions.

Use the multiplication rule to find the probability that the first three guesses are wrong and the fourth is correct. That is, find
P(WWWC) , where C denotes a correct answer and W denotes a wrong answer.
(round answer to 4 decimal places) 

P(wwwc)=

Answer 1

Since each question has 5 choices, the probability of getting the right answer on any one question is:

(# of correct choices)/(total number of choices)=1/5

 

The probability of choosing the wrong answer is:

(# of incorrect choices)/(total number of choices)=4/5

 

This is also equal to:

1-P(correct)=1-1/5=4/5

 

Since we want to know the probability of getting the 1st 3 right and the 4th one wrong:

(1/4)(1/4)(1/4)(3/4)=3/256

 

This is because we multiply the probabilities of each individual event by each other when we want "this AND that AND that".