document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167040>Question 1167040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, if someone could help me solve this problem/explain to me the steps, that would be very helpful. Thank you so much.\r<BR>\n" );
document.write( "\n" );
document.write( "G and H are mutually exclusive events.\r<BR>\n" );
document.write( "\n" );
document.write( "P(G) = 0.5\r<BR>\n" );
document.write( "\n" );
document.write( "P(H) = 0.3\r<BR>\n" );
document.write( "\n" );
document.write( "P(H|G) = 0.6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "    1. Find P(H OR G).\r<BR>\n" );
document.write( "\n" );
document.write( "    2. Are G and H independent or dependent events. Why?\r<BR>\n" );
document.write( "\n" );
document.write( "I mostly just need help finding P (H OR G). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791610 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52814)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "P(H|G) = 0.6 means that  the ratio  P(H &#8745; G) / P(G) = 0.6  (by the definition of conditional probability).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute here the given data, and you will get\r\n" );
document.write( "\r\n" );
document.write( "    P(H &#8745; G) / 0.5 = 0.6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies  P(H &#8745; G) = 0.5*0.6 = 0.3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Finally, use the general probability formula for the union\r\n" );
document.write( "\r\n" );
document.write( "    P(H OR G) = P(H) + P(G) - P(H &#8745; G),\r\n" );
document.write( "\r\n" );
document.write( "which is valid for any events H and G.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute all given and found values into this formula, and you will get\r\n" );
document.write( "\r\n" );
document.write( "    P(H OR G) = 0.3 + 0.5 - 0.3 = 0.5.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved and explained in all details.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In this site, there are two lessons for problems on <U>conditional probability</U>.  They are\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-conditional-probability-problems.lesson>Conditional probability problems REVISITED</A> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Solved problems on Probability</U>\" <BR>\n" );
document.write( "and &nbsp;\"<U>Additional problems on Probability</U>\". \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "into your archive and use when it is needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );