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:

Nutritional Assessment

The analysis of various health factors to determine a person's nutritional status and dietary needs.

Overweight

A condition characterized by having more body weight than is considered normal or healthy for a certain height, often due to excess body fat.

Fat

A natural oily substance occurring in animal bodies, especially when deposited as a layer under the skin or around certain organs.

Taste

A sense that enables the detection of flavors in substances, primarily through sensory organs on the tongue.