In an optical sensory experiment, a subject shows a fast response (F), a delayed response (D), or no response at all (N). The experiment will be performed on two subjects.
(a) Using a tree diagram, list the sample space.
(b) Suppose, for each subject, P(F) = -4, P(D) = .3, P(N) = .3, and the responses of different subjects are independent.
(i) Assign probabilities to the elementary outcomes.
(ii) Find the probability that at least one of the subjects shows a fast response.
(iii) Find the probability that both of the subjects respond.