Question

In Exercises $1-8$, use Bayes' theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. $P(A \mid B)=.8, P(B)=.2, P\left(A \mid B^{\prime}\right)=.3 .$ Find $P(B \mid A)$

Name: Problem 1, Chapter 7: Finite Mathematics and Applied Calculus
Uploaded: 2021-10-21T17:12:18-08:00
Duration: 1 min 20 s
Channel: Lucas Finney
Description: In Exercises 1-8, use Bayes' theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. P(A |B)=.8, P(B)=.2, P(A |B^')=.3 . Find P(B |A)

   In Exercises $1-8$, use Bayes' theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. 
$P(A \mid B)=.8, P(B)=.2, P\left(A \mid B^{\prime}\right)=.3 .$ Find $P(B \mid A)$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 7, Problem 1

Instant Answer

Solved by Expert Lucas Finney

10/21/2021

Step 1

We are given that $P(A \mid B)=0.8$, $P(B)=0.2$, and $P\left(A \mid B^{\prime}\right)=0.3$. We also know that the probability of the complement of B, $P(B^{\prime})$, is $1 - P(B) = 1 - 0.2 = 0.8$. Show more…

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In Exercises $1-8$, use Bayes' theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. $P(A \mid B)=.8, P(B)=.2, P\left(A \mid B^{\prime}\right)=.3 .$ Find $P(B \mid A)$

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Key Concepts

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another related event has already occurred. It forms the basis for understanding dependent events and updating probabilities based on new information.

Law of Total Probability

The law of total probability provides a way to break down complex probability problems into simpler parts by considering all possible scenarios that cover the entire sample space. It is particularly useful when calculating the overall probability of an event that can happen in multiple disjoint ways.

Bayes' Theorem

Bayes' theorem is a fundamental result in probability theory that relates the conditional and marginal probabilities of random events. By reversing the conditioning – that is, turning P(A|B) into P(B|A) – it allows for the updating of beliefs in the light of new evidence and is crucial in decision making and statistical inference.

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