A Medical Test Has Been Designed to Detect the Presence

question 166

Short Answer

A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the test is 0.99. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.02. It is estimated that 7% of the population who take this test have the disease.
If necessary, round your answers to three decimal places.
If the test administered to an individual is positive, what is the probability that the person actually has the disease?
__________
If an individual takes the test twice and both times the test is positive, what is the probability that the person actually has the disease?
__________

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Definitions:

Leadership Office

A position or role within an organization charged with guiding and influencing employees or members towards achieving collective goals.

Open-Book Management

A business strategy where employees are provided with company financial information to help them make better decisions and understand how their actions affect the company's performance.

Participative Management

A management style in which employees at all levels are encouraged to contribute ideas towards identifying and solving problems, making decisions, and setting goals.

Jack Stack

A business leader and author known for pioneering the concept of open-book management and the principle of teaching employees about finance and business strategies.