Three doctors, Doctor A, Doctor B and Doctor C work at a family medicine practic

Question

Three doctors, Doctor A, Doctor B and Doctor C work at a family medicine practice. The probability that you can get a same-day appointment with them is 0.5, 0.7 and 0.8 respectively. The three events are independent of each other.

Doctor A has been your family physician for many years, so you check if you can get an appointment with her first. If you fail, you ask Doctor B. If you fail to get an appointment with Doctor B, you then ask Doctor C.

What is the probability that you do not get a same-day appointment?

Given that you got a same-day appointment, what is probability that it was with your family doctor (Doctor A)?

Explanation / Answer

What is the probability that you do not get a same-day appointment?

Probability = 1 - (0.5*0.7*0.8) = 0.72

Given that you got a same-day appointment, what is probability that it was with your family doctor (Doctor A)?

Probability = 0.3*0.2*0.5 / 0.5 = 0.06

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