Use Bayes's Rule to Find the Indicated Probability

question 36

Multiple Choice

Use Bayes's rule to find the indicated probability.
-A person must select one of three boxes, each filled with clocks. The probability of box A being selected is 0.33, of box B being selected is 0.17, and of box C being selected is 0.5. The probability of Finding a red clock in box A is 0.2, in box B is 0.4, and in box C is 0.9. A box is selected. Given that
The box contains a red clock, what is the probability that box A was chosen?

• A)0.066
• B)0.33
• C)0.133
• D)0.113

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Definitions:

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A theory in ethics and philosophy asserting that moral standards are derived from human nature and the natural world, holding universal applicability.

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Referring to an individual's ability to operate or perform at their maximum potential in physical, mental, or emotional capacities.

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A reference to Immanuel Kant, an 18th-century German philosopher known for his work in ethics and moral philosophy, emphasizing duty, autonomy, and the categorical imperative.