An animal either dies (D) or survives (S) in the course of a surgical experiment. The experiment is to be performed first with two animals. If both survive, no further trials are to be made. If exactly one animal survives, one more animal is to undergo the experiment. Finally, if both animals die, two additional animals are to be tried.
(a) List the sample space.
(b) Assume that the trials are independent and the probability of survival in each trial is 4. Assign probabilities to the elementary outcomes.
(c) Let X denote the number of survivors. Obtain the probability distribution of X by referring to part (b).