Question

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 are O1 = (C, C), 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) What outcomes are contained in A, the event that at most one patient is covered? A = {(C, C), (C, N), (N, N)} A = {(C, C), (N, C), (N, N)} A = {(C, N), (N, C)} A = {(C, N), (N, C), (N, N)} A = {(C, C), (C, N), (N, C)}

What is P(A)? P(A) =

(b) What outcomes are contained in B, the event that the two patients have different statuses with respect to coverage? B = {(C, C), (C, N)} B = {(C, C), (N, N)} B = {(C, N), (N, C)} B = {(C, N), (N, N)} the empty set

What is P(B)? P(B) =

Answer 1

a) The event that at most one patient is covered is,

A = {(C, N), (N, C), (N, N)}

P(A) = P(O2) + P(O3) + P(O4)

= 0.09 + 0.09 + 0.01 = 0.19

b) The event that the two patients have different statuses with respect to coverage is

B = {(C, N), (N, C)}

P(B) = P(O2) + P(O3)

= 0.09 + 0.09 = 0.18