document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262826>Question 262826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't even know how to set up this problem. I am not finding examples, can you help please? \r<BR>\n" );
document.write( "\n" );
document.write( "Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3<BR>\n" );
document.write( "and P(A or B) = 0.75, find P(B).<BR>\n" );
document.write( "(B) Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or<BR>\n" );
document.write( "B) = 0.72, find P(A and B) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193598 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(a or b) = p(a) + p(b) if a and b are mutually exclusive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if p(a) = .3 and p(a or b) = .75, then p(b) must be equal to .75 - .3 = .45\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get p(a or b) = p(a) + p(b) = .3 + .45 = .75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your second problem states that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(a) = .3<BR>\n" );
document.write( "p(b) = .5<BR>\n" );
document.write( "p(a or b) = .72\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "find p(a and b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in this example, apparently a and b are not mutually exclusive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p (a or b) = p(a) + p(b) - p(a and b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on that,  your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".72 = .3 + .5 - p(a and b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".72 = .8 - p(a and b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add p(a and b) to both sides of this equation and subtract .72 from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(a and b) = .8 - .72 = .08\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answer is p(a and b) = .08\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference that shows you how it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://people.richland.edu/james/lecture/m170/ch05-rul.html\" target = \"_blank\">http://people.richland.edu/james/lecture/m170/ch05-rul.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what is happening when events a and b are not mutually exclusive is that you can have cases where both events a and b occur simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when that happens, they are being counted twice if you just add up p(a) + p(b).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by subtracting p(a and b), you are eliminating the double counting.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );