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

To find the probability that a patient arriving by ambulance has Medicare insurance, we need to use Bayes' theorem. Let's denote the event that a patient has Medicare insurance as M and the event that a patient arrives by ambulance as A. Then, we can calculate P(M|A) as follows:

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

We are given that P(M) = 0.3 and P(M') = 0.7. We are also given that P(A|M) = 0.2 and P(A|M') = 0.1. Substituting these values, we get:

P(M|A) = 0.2 * 0.3 / (0.2 * 0.3 + 0.1 * 0.7) = 0.4615

Therefore, the probability that a patient arriving by ambulance has Medicare insurance is 0.4615 or 46.15%. The closest answer choice to this value is C (46.15% rounded to the nearest whole number).

At Dolon General Hospital, 30 Percent of the Patients Have