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) P(WWWC) , where C denotes a correct answer and W denotes a wrong answer. (round answer to 4 decimal places) P(WWWC)= P(WWWC)= What is the probability of getting exactly one correct answer when 4 guesses are made? (round answer to 4 decimal places) P(exactly one correct answer) =

Answer 1

P(correct guessing) P(C)= 1/5 = 0.2 [as total 5 options in which one is correct]

P(wrong answer)=P(W)=1-0.2=0.8

P(first three guesses are wrong) and fourth is correct=P(WWWC) = 0.8*0.8*0.8*0.2=0.1024

P(exactly one correct answer)=4C1*0.2*0.8³ = 0.4096