SOLUTION: How do I find P(B∩A�)? For example, I have P(B) = 0.60. I know the following information: P(A|B)=0.30. P(B|A)=0.60. P(A∩B)=0.18. So would P(B∩A�) be 0.60 + 1-P(A)

Question 1117717: How do I find P(B∩A�)? For example, I have P(B) = 0.60. I know the following information: P(A|B)=0.30. P(B|A)=0.60. P(A∩B)=0.18. So would P(B∩A�) be 0.60 + 1-P(A)? Also, what would A be?

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

As I read your question, the actual given information is

P(A|B)=0.30; P(B|A)=0.60; P(A and B)=0.18.

I personally find it easiest to see what is going on in this kind of problem using a Venn diagram.

Whether with a Venn diagram or with symbols, P(A|B)=0.30 means that P(A and B) is only 0.30 times P(B):

0.18 = 0.30*P(B) --> P(B) = 0.18/0.30 = 0.60

Then since P(B) is 0.60 and P(A and B) is 0.18, P(B and A') is 0.60-0.18 = 0.42.

Similarly, P(A and B)=0.18 and P(B|A)=0.60 means

0.18 = 0.60*P(A) --> P(A) = 0.18/0.60 = 0.30

and that makes P(A and B') = 0.30-0.18 = 0.12.

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The preceding is a formal way of solving your problem.

Now here is the actual method I used for getting the answer of P(B and A')=0.42.

(Look at a Venn diagram to follow the logic of this method.)

Since P(A|B)=0.30, P(A'|B)=0.70.

Then the ratio of P(B and A') to P(B and A) is 0.70:0.30.

And so P(B and A') is
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SOLUTION: How do I find P(B&#8745;A�)? For example, I have P(B) = 0.60. I know the following information: P(A|B)=0.30. P(B|A)=0.60. P(A&#8745;B)=0.18. So would P(B&#8745;A�) be 0.60 + 1-P(A)

SOLUTION: How do I find P(B∩A�)? For example, I have P(B) = 0.60. I know the following information: P(A|B)=0.30. P(B|A)=0.60. P(A∩B)=0.18. So would P(B∩A�) be 0.60 + 1-P(A)