Three friends Alan, Roger and Peter attempt to answer a question on an exam. Alan randomly guesses the answer, giving him a 1/5 probability of guessing correctly. Roger cheats by looking at the paper of the student in front of him, giving him a 2/3 probability of answering correctly. And Peter dutifully performs the calculations, then marks the answer, giving him a 5/6 probability of a correct answer. What is the probability that the question is answered correctly, but not via cheating? Choices:
A) 1/18
B) 1/9
C) 23/90
D) 5/18
E) 13/45
Prob(1/18lan) = 1/5   Prob(Roger) without cheating = 2/3-1 = 1/3   Prob(Peter) = 5/6   Total Probability = 1/5*1/3*/5/6 = 1/18   1/18nswer is 1/18
<result>A</result>
Three friends Alan, Roger and Peter attempt to answer a question on an exam. Alan randomly guesses the answer, giving him a 1/5 probability of guessing correctly. Roger cheats by looking at the paper of the student in front of him, giving him a 2/3 probability of answering correctly. And Peter dutifully performs the calculations, then marks the answer, giving him a 5/6 probability of a correct answer. What is the probability that the question is answered correctly, but not via cheating?