Insurance status—covered ( C ) or not covered ( N )—is determined for each indiv

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

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

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

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

e) 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 the same status with respect to coverage?

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

b) B = {(C, C), (N, N)}     

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

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

e) the empty set

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

Explanation / Answer

1. is A = {(C, C), (C, N), (N, C)} and P(A) = 0.81+0.09+0.09 = .99

2. B = {(C, C), (N, N)} and P(B) = 0.81+0.01 = 0.82

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