At Dolon General Hospital,30 percent of the patients have Medicare insurance (M)while 70 percent do not have Medicare insurance (M´).Twenty percent of the Medicare patients arrive by ambulance,compared with 10 percent of the non-Medicare patients.If a patient arrives by ambulance,what is the probability that the patient has Medicare insurance?

Question

Quizplus · Accepted Answer

We need to find the probability of a patient having Medicare insurance given that they arrived by ambulance. This can be found using Bayes' theorem:

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

Where:
P(M | A) = Probability of having Medicare insurance given that the patient arrived by ambulance
P(A | M) = Probability of arriving by ambulance given that the patient has Medicare insurance (0.20)
P(M) = Probability of having Medicare insurance (0.30)
P(A) = Probability of arriving by ambulance (0.20*0.30 + 0.10*0.70 = 0.13)

Plugging in the values, we get:

P(M | A) = (0.20 * 0.30) / 0.13
P(M | A) = 0.4615

Therefore, the probability of a patient having Medicare insurance given that they arrived by ambulance is 0.4615, or approximately 46.15%. The best choice is C.

At Dolon General Hospital,30 Percent of the Patients Have Medicare