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A medical practice group consists of seven doctors, four women and three men. The women are Drs. Town, Wu, Hein, and Lee. The men are Drs. Marland, Penner, and Holmes. Suppose new patients are randomly assigned to one of the doctors in the group. a. List the equally likely outcomes that could occur when a patient is assigned to one of the doctors. b. What is the probability that the new patient is assigned to a female doctor? Write your answer as a fraction and as a percentage rounded to one decimal place. c. What is the probability that the new patient will be assigned to a male doctor? Write your answer as a fraction and as a percentage rounded to one decimal place. d. Are the events described in parts (b) and (c) complements? Why or why not?

Step by step solution

01

List Equally Likely Outcomes

In this case, the equally likely outcomes occur when a patient is assigned to any of the seven doctors, irrespective of their gender. Thus, the seven outcomes are: [Town, Wu, Hein, Lee, Marland, Penner, Holmes].

02

Probability of a Female Doctor

The group has four female doctors. So, out of seven doctors, the probability that a new patient is assigned to a female doctor is \(\frac{4}{7}\). This can be converted to percentage by multiplying by 100, which gives approximately 57.1%.

03

Probability of a Male Doctor

The group has three male doctors. So, out of seven doctors, the probability that a new patient is assigned to a male doctor is \(\frac{3}{7}\). This can be converted to percentage by multiplying by 100, which gives approximately 42.9%.

04

Identify Complementary Events

Two events are complementary if they add up to yield a probability of 1 (or 100% if we’re dealing with percentages). Here, the event of a patient being assigned to a female doctor and the event of a patient being assigned to a male doctor are the only two possibilities and together make up the complete set of outcomes. Thus, their probabilities should add up to 1, which they do (\(\frac{4}{7} + \frac{3}{7} = 1\)). Hence, these two events are complementary.

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