Question

Your subjective degree of belief in $B$ is 0.1 and your degree of belief in $A$ given $B$ is 0.4 . You then come to believe that the unconditional probability of $A$ is 0.90 . To what degree should you believe $B$ given $A$ ? (That is, what is $p(B \mid A) ?$ ?)

Name: Problem 2, Chapter 10: An Introduction to Decision Theory
Uploaded: 2021-12-25T15:54:52-08:00
Duration: 1 min 28 s
Channel: Christopher Stanley
Description: Your subjective degree of belief in B is 0.1 and your degree of belief in A given B is 0.4 . You then come to believe that the unconditional probability of A is 0.90 . To what degree should you believe B given A ? (That is, what is p(B |A) ? ?)

   Your subjective degree of belief in $B$ is 0.1 and your degree of belief in $A$ given $B$ is 0.4 . You then come to believe that the unconditional probability of $A$ is 0.90 . To what degree should you believe $B$ given $A$ ? (That is, what is $p(B \mid A) ?$ ?)

An Introduction to Decision Theory

Martin Peterson 1st Edition

Chapter 10, Problem 2

Instant Answer

Solved by Expert Christopher Stanley

12/25/2021

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1. This means that before considering any evidence or information, you have a low degree of belief in $B$. Show more…

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Your subjective degree of belief in $B$ is 0.1 and your degree of belief in $A$ given $B$ is 0.4 . You then come to believe that the unconditional probability of $A$ is 0.90 . To what degree should you believe $B$ given $A$ ? (That is, what is $p(B \mid A) ?$ ?)

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Key Concepts

Conditional Probability

Conditional probability quantifies the likelihood of an event occurring given that another event has occurred, and is represented as p(A|B). It is a fundamental concept in probability theory and is essential for understanding how probabilities update when new information is available.

Bayes' Theorem

Bayes' Theorem is a foundational principle in probability that provides a method for updating beliefs in light of new evidence. It relates the conditional and marginal probabilities of events, typically expressed as p(B|A) = p(A|B) * p(B) / p(A), and is widely used in statistical inference and decision-making.

Subjective Probability

Subjective probability refers to an individual's personal judgment or degree of belief about the occurrence of an event. Unlike objective probabilities derived from long-run frequencies, subjective probabilities allow for personal opinions and evidence to influence the estimation of likelihoods.

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