Medical insurance status—covered (C) or not covered (N)—is determined for each individual arriving for treatment at a hospital’s emergency room. Consider the chance experiment in which this determination is made for two randomly selected patients.

The simple events for this chance experiment are O₁ = (C, C), meaning that the first patient selected was covered and the second patient selected was also covered, O₂ = (C, N), O₃ = (N, C), and O₄ = (N, N). Suppose that probabilities are P(O₁) = 0.81, P(O₂) = 0.09, P(O₃) = 0.09, and P(O₄) = 0.01.

a. Define A as the event that at most one patient is covered.

i. What simple events are in the event A?

ii. Calculate P(A).

b. Define B as the event that the two patients have the same coverage status.

i. What simple events are in the event B?

ii. Calculate P(B).