Question

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]

P(A | B) = .2, P(B) = .1, P(A | B') = .6. Find P(B | A).

P(B | A) =

Answer 1

Bayes Theorem is based on the information of the past observation. The previous information given is prior information and the probability associated to it give prior praobability. Once the information for the data i.e. likelihood information is used it gives posterior information and the probability associated to it is posterior probability.

Let B be denote the prior event then we have prior probability as P(B)=0.1.

Let A be any event associated and it is generally likelihood information.

Then (B|A) is the posterior event and the probability associated to it is obatined using Baye's theorem given by

We have P(B)=0.1. Therefore, we have

Since, P(A|B)=0.2, P(A|B')=0.6. Therefore, the P(B|A) is given by

Therefore the P(B|A) is 0.0357.