document.write( "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?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #732923 by greenestamps(13203)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "As I read your question, the actual given information is

\n" ); document.write( "P(A|B)=0.30; P(B|A)=0.60; P(A and B)=0.18.

\n" ); document.write( "I personally find it easiest to see what is going on in this kind of problem using a Venn diagram.

\n" ); document.write( "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):

\n" ); document.write( "0.18 = 0.30*P(B) --> P(B) = 0.18/0.30 = 0.60

\n" ); document.write( "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.

\n" ); document.write( "Similarly, P(A and B)=0.18 and P(B|A)=0.60 means

\n" ); document.write( "0.18 = 0.60*P(A) --> P(A) = 0.18/0.60 = 0.30

\n" ); document.write( "and that makes P(A and B') = 0.30-0.18 = 0.12.

\n" ); document.write( "------------------------------------------------------

\n" ); document.write( "The preceding is a formal way of solving your problem.

\n" ); document.write( "Now here is the actual method I used for getting the answer of P(B and A')=0.42.

\n" ); document.write( "(Look at a Venn diagram to follow the logic of this method.)

\n" ); document.write( "Since P(A|B)=0.30, P(A'|B)=0.70.

\n" ); document.write( "Then the ratio of P(B and A') to P(B and A) is 0.70:0.30.

\n" ); document.write( "And so P(B and A') is \"%28%280.70%29%2F%280.30%29%29%2A0.18+=+0.42\" \n" ); document.write( "
\n" );