use bayes theorem or a tree diagram to calculate the indicated probability round your answer to

First, we need to find P(A). We can use the law of total probability for this, which states that

Use bayes theorem or a tree diagram to calculate the...

Transcript

00:01 In this problem, we're given the probability that a occurs given that b has occurred is 0 .5, the probability that b occurs is 0 .9, and the probability that a occurs given that the complement of b has occurred is 0 .4.

00:14 Our job is to find the probability that b occurs given that a has occurred.

00:20 We will use bayes ' theorem, which states that the probability that a occurs given that b occurs is the probability of their intersection divided by the probability of the second event, in this case, the probability of b.

00:42 So we know two of the three parts of this formula in this problem.

00:48 We know the left -hand side is 0 .5.

00:53 We know that the probability that b occurs is 0 .9.

00:58 So what we can solve for is the probability that a intersect b occurs.

01:06 So we see that the probability that a intersect b occurs is simply the product of those two probabilities, or 0 .45.

01:21 All right, and we will need that answer in just a minute.

01:26 So what's the next step in this problem? we will apply the same formula, but the second application, we will use the version, the probability that a occurs given that b complement has occurred.

01:41 So let's apply this again.

01:43 Let's come down here and do that.

01:46 Here we have the probability that a occurs given that b complement occurs is the probability of their intersection divided by the probability that b complement occurs.

02:02 Now, we know two of these three.

02:05 We are given that the probability that a occurs given that b complement occurs is 0 .4.

02:12 We don't know the probability of the intersection.

02:16 If we look back at the problem at first glance, it may seem like we are not given this information.

02:22 But we are told that the probability that b does occur is 0 .9.

02:26 That means the probability that b does not occur, the probability of its complement is 1 minus that, or 0 .1...

Question

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. P(A | B) = 0.5, P(B) = 0.9, P(A | B') = 0.4. Find P(B | A).

Question

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. P(A | B) = 0.5, P(B) = 0.9, P(A | B') = 0.4. Find P(B | A).

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