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, 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.