How to do Bayes' theorem?

Question

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. P(A | B) = .9, P(B) = .6, P(A | B') = .8. Find P(B | A).

We don't have an example like this in class so I was wondering if someone could help me figure out how to solve it.

Here are a couple of hints: State Bayes's Theorem. Can you calculate $P(B^\prime)$, which is the complement of $P(B)$? How about $P(A)$? Can you use Bayes' theorem now? — Larry B., Oct 21 '16 at 22:03

score 2 · Accepted Answer · answered Oct 21 '16 at 22:19

2

Bayes theorem:

$$P(B|A)=\frac{P(A|B)P(B)}{P(A)}$$

So you only need to find $P(A)$. Use the law of total probability:

$$P(A)=P(A|B)P(B)+P(A|B')P(B')$$

and notice that $$P(B')=1-P(B)$$

answered Oct 21 '16 at 22:19

msm

7,147

Thank you so much for explaining that all out like that, I seriously appreciate it – user344249 Oct 21 '16 at 22:21
I am glad that it helped @user344249 – msm Oct 21 '16 at 22:25

How to do Bayes' theorem?

1 Answers1