Question

A head cardiovascular surgeon submits the following tables describing procedures that his department completed and the insurance information for one quarter at a local hospital.

Insurance Type	Count
VA	41
Medicaid	276
Medicare	384
Private	72

Procedure	Count
Heart Valve Repair	117
Arrhythmia Treatment	211
Heart Transplant	22
Coronary Bypass	423

a. What is the probability that, if chosen at random, a patient will be covered by Medicare insurance? 

b. What is the probability of receiving arrhythmia treatment?  

c. What can we say about these events? Provide evidence. 

Answer 1

total number of patients = 41+276+384+72 = 773

a)

That's absolutely correct ,they asked directly ( there is no conditional probability in question)

Than answer must be = 384c1/773c1

=0.496765847

=0.4968

b)

P(A/M) = P(A and M)/P(M)

=>

Probabilty of receiving arrhythmia treatment and medicare coverage

= P(A/M) * P(M)

= 0.64 * 0.4968

= 0.318

c)

probability of receiving arrhythmia treatment

=211/773

= 0.273