Refer to Exercise 5.49. Now suppose for each plot a fair coin is tossed. If a head shows up, the plot is treated; otherwise, it is a control. With this manner of treatment allocation, answer parts (a) and (b).
In Exercise 5.49
From four agricultural plots, two are selected at random for a pesticide treatment. The other two plots serve as controls. For each plot, denote by S the event that it is treated with the pesticide. Consider the assignment of treatment or control to a single plot as a trial.
(a) Is P(S) the same for all trials? If so, what is the numerical value of P(S)?
(b) Are the trials independent? Why or why not?