Use Bayes' theorem or a tree diagram to calculate the...

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. P(A | B) = 0.2, P(B) = 0.4, P(A | B') = 0.9. Find P(B | A). P(B | A) =

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Transcript

00:01 Here let's draw a tree diagram.

00:02 It's a bit clearer than base theorem.

00:05 So start off with event b, and we know the outcome for b.

00:11 So b and not b.

00:14 B is 0 .4.

00:17 That's from here.

00:18 That we're told in the question.

00:21 So not be then must be 0 .6, 1 minus 0 .4.

00:26 Remember tree diagrams, the branches add to give you 1.

00:31 Now we're told here that p of a given b is a occurred is 0 .2.

00:36 So here then we have events a and not a and we know here is 0 .2, a given b.

00:46 B has happened, so we're here.

00:49 So a happening is 0 .2, which means here it must be 0 .8.

00:53 Again, 1 minus 0 .2.

00:56 Here we're told p of a given b is not occurred is 0 .9.

01:00 So let's go a branch here.

01:02 A not a.

01:04 Here is 0 .9.

01:06 So here is 0 .1.

01:11 Now, we know that p of a and b in general is equal to p of event a times p of event b, given that a has occurred.

01:28 That you will find on all formula sheets, standard formula.

01:34 I want to work out this one here that i want to find.

01:40 This i can work out, p of a and b, from up here.

01:46 This one is a and b...

Question

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. P(A | B) = 0.2, P(B) = 0.4, P(A | B') = 0.9. Find P(B | A). P(B | A) =

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