document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119956>Question 1119956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this in simple way. Thank You.\r<BR>\n" );
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document.write( "Suppose that A and B are two events for which P(A)=0.25, P(B)=0.73, and P(B|A)=0.52 Find each of the following:\r<BR>\n" );
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document.write( "A. P(AandB)= <BR>\n" );
document.write( "B. P(AorB)= <BR>\n" );
document.write( "C. P(A|B)=  </SPAN>\n" );
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document.write( "The formal definition of conditional probability is<br><BR>\n" );
document.write( "P(A|B) = (P(A and B))/(P(B))<br><BR>\n" );
document.write( "Then P(A and B) = (P(A|B))*P(B).<br><BR>\n" );
document.write( "So in your example, P(A and B) = (0.52)(0.25) = 0.13.<br><BR>\n" );
document.write( "That makes P(A or B) = (0.25+0.73)-0.13 = 0.85; and P(A|B) = P(A and B)/P(B) = 0.13/0.73 = (approximately) 0.178.<br><BR>\n" );
document.write( "I personally find the formal definition of conditional probability confusing.<br><BR>\n" );
document.write( "My way of thinking of P(B|A) is that the sample space is only \"A\", and I want to know what part of A is also B.  That makes it easy (for me!) to see that P(A and B) is equal to P(B|A) times P(A).<br><BR>\n" );
document.write( "A picture with a Venn diagram can also help visualize the probabilities, if you are thinking of A as the sample space.  In your example, P(A) is 0.25, and P(B|A) is 0.52 of A, or 0.52*0.25 = 0.13 </SPAN>\n" );
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