document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952345>Question 952345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Sam can get a grant to support her program, she feels that there is a .9 probability that the program will work. If she fails to get the grant, she feels that there will only be a .3 probability that it will be successful. If the probability of getting the grant is .6, what is the probability of success?\r<BR>\n" );
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document.write( "I have tried all kinds of distribution tables, and still cant seem to get it correct. PLEASE HELP. You dont have to give me the answer, just tell me what steps I need to figure it out. \r<BR>\n" );
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document.write( "Thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581587 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=581587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notation/Variable Setup:\r<BR>\n" );
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document.write( "G = gets a grant<BR>\n" );
document.write( "W = program will work\r<BR>\n" );
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document.write( "P(G) = probability she gets the grant<BR>\n" );
document.write( "P(G')= probability she doesn't get the grant\r<BR>\n" );
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document.write( "P(W|G) = probability program works IF she gets grant<BR>\n" );
document.write( "P(W|G') = probability program works IF she does NOT get grant\r<BR>\n" );
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document.write( "\"what is the probability of success? \" translation: \"what is the probability of the program works, ie, what is P(W)? \"\r<BR>\n" );
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document.write( "To compute P(W), we use the <a  rel=nofollow HREF=\"http://people.reed.edu/~jones/Courses/P02.pdf\">law of total probability</a>, which in this specific case means: P(W) = P(W|G)*P(G) + P(W|G')*P(G')\r<BR>\n" );
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document.write( "So we need to find the following\r<BR>\n" );
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document.write( "P(W|G)<BR>\n" );
document.write( "P(W|G')<BR>\n" );
document.write( "P(G)<BR>\n" );
document.write( "P(G')\r<BR>\n" );
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document.write( "So let's pick through the problem to pull out the needed info\r<BR>\n" );
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document.write( "\"If Sam can get a grant to support her program, she feels that there is a .9 probability that the program will work\", so P(W|G) = 0.9\r<BR>\n" );
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document.write( "\"If she fails to get the grant, she feels that there will only be a .3 probability that it will be successful\", so P(W|G') = 0.3\r<BR>\n" );
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document.write( "P(G) = 0.6 because \"the probability of getting the grant is .6\"<BR>\n" );
document.write( "P(G') = 0.4 because 1-0.6 = 0.4\r<BR>\n" );
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document.write( "Summary of what we're given\r<BR>\n" );
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document.write( "P(W|G) = 0.9<BR>\n" );
document.write( "P(W|G') = 0.3<BR>\n" );
document.write( "P(G) = 0.6<BR>\n" );
document.write( "P(G') = 0.4\r<BR>\n" );
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document.write( "Now we plug all this into the equation P(W) = P(W|G)*P(G) + P(W|G')*P(G') to get...\r<BR>\n" );
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document.write( "P(W) = P(W|G)*P(G) + P(W|G')*P(G')\r<BR>\n" );
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document.write( "P(W) = 0.9*0.6 + 0.3*0.4\r<BR>\n" );
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document.write( "P(W) = 0.54 + 0.12\r<BR>\n" );
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document.write( "P(W) = 0.66\r<BR>\n" );
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document.write( "The final answer is 0.66\r<BR>\n" );
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document.write( "If you need more one-on-one help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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