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" );
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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 #193595 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have a general formula to help us:<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28A+u+B%29+=+p%28A%29+%2B+p%28B%29+-+p%28A+n+B%29 ALIGN=MIDDLE  ALT=\"p%28A+u+B%29+=+p%28A%29+%2B+p%28B%29+-+p%28A+n+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p(a u B) means probability of A union B. Union is another word for \"OR\"<BR>\n" );
document.write( "p(A n B) means probability of A intersection B. Intersection is another word for \"AND\"<BR>\n" );
document.write( "since events A and B are mutually exclusive, there will be no overlap and there fore, p(A n B) = 0.<BR>\n" );
document.write( "From above and this information, we get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.75+=+.3+%2B+p%28B%29+%2B+0 ALIGN=MIDDLE  ALT=\".75+=+.3+%2B+p%28B%29+%2B+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for p(B), we get<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28B%29+=+.45 ALIGN=MIDDLE  ALT=\"p%28B%29+=+.45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "part (B):<BR>\n" );
document.write( "using the same formula as<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28A+u+B%29+=+p%28A%29+%2B+p%28B%29+-+p%28A+n+B%29 ALIGN=MIDDLE  ALT=\"p%28A+u+B%29+=+p%28A%29+%2B+p%28B%29+-+p%28A+n+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the given information, we get<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.72+=+.30+%2B+.50+-+p%28A+n+B%29 ALIGN=MIDDLE  ALT=\".72+=+.30+%2B+.50+-+p%28A+n+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28A+n+B%29+=+.08 ALIGN=MIDDLE  ALT=\"p%28A+n+B%29+=+.08\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this means there is a slight overlap of the 2 sets.<BR>\n" );
document.write( "hope this helps. </SPAN>\n" );
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