A Sample Is Selected from One of Two Populations, S₁

question 72

Short Answer

A sample is selected from one of two populations, S₁ and S₂, with probabilities P(S₁) = 0.80 and P(S₂) = 0.20. If the sample has been selected from S₁, the probability of observing an event A is P(A / S₁) = 0.15. Similarly, If the sample has been selected from S₂, the probability of observing A is P(A / S₂) = 0.25.
Round your answer to four decimal places, if necessary
a. If a sample is randomly selected from one of the two populations, what is the probability that event A occurs?
______________
If a sample is randomly selected and event A is observed, what is the probability that the sample was selected:
b. From population S₁?
______________
c. From population S₂?
______________

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Definitions:

Disease Development

The process through which a condition or illness begins and progresses within the body.

Physiological Diseases

Disorders that affect the body's organs and systems, causing them to function improperly.

Immune System

The body's defense mechanism against pathogens, comprising cells, tissues, and organs that work together to safeguard health.

Cardiovascular Disease (CVD)

Disorders of the circulatory system, including coronary artery disease and stroke.