Insurance status - covered ( C ) or not covered ( N ) - is determined for each i

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) = .81, P(O2) = .09, P(O3) = .09, and P(O4) = .01.

(a) What outcomes are contained in A, the event that at most one patient is covered, and what is P(A)?

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)}

P(A) =  
(b) What outcomes are contained in B, the event that the two patients have the same status with respect to coverage, and what is P(B)?

B = {(C, C), (C, N)}B = {(C, C), (N, N)}    B = {(C, N), (N, C)}B = {(C, N), (N, N)}the empty set

Explanation / Answer

A = at most one patient is covered

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

P(A) = P(C,N)+P(N,C)+P(N,N) ( composite event is a summation of simple events)

= 0.09+0.09+0.01 = 0.19

(b) B = 2 patients have the same status

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

P(B) = P(C,C) + P(N,N)

= 0.81+0.01 = 0.82

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