document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150018>Question 1150018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mathematics professor assigns two problems for homework and knows that the probability of a student solving the first problem is 0.85, the probability of solving the second is 0.45, and the probability of solving both is 0.05. (Round your answers to three decimal places.)\r<BR>\n" );
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document.write( "(a) Jed has solved the second problem. What is the probability he also solves the first problem?\r<BR>\n" );
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document.write( "(b) Edna has solved the first problem. What is the probability she also solves the second problem?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771361 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=771361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "A = event of solving the first problem<BR>\n" );
document.write( "B = event of solving the second problem\r<BR>\n" );
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document.write( "Given <BR>\n" );
document.write( "P(A) = 0.85<BR>\n" );
document.write( "P(B) = 0.45<BR>\n" );
document.write( "P(A and B) = 0.05\r<BR>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "Jed has solved the second problem. So we're given that event B has happened. We want to find P(A|B) which is the probability of event A happening given B has happened.\r<BR>\n" );
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document.write( "Use the conditional probability formula<BR>\n" );
document.write( "P(A|B) = P(A and B)/P(B)<BR>\n" );
document.write( "P(A|B) = 0.05/0.45<BR>\n" );
document.write( "P(A|B) = 0.111111<BR>\n" );
document.write( "P(A|B) = 0.111\r<BR>\n" );
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document.write( "Answer: 0.111<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Same idea as in part (a), but now we want to find P(B|A). We know event A has happened and we want to find the probability of event B happening based on A. \r<BR>\n" );
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document.write( "P(B|A) = P(B and A)/P(A)<BR>\n" );
document.write( "P(B|A) = P(A and B)/P(A)<BR>\n" );
document.write( "P(B|A) = 0.05/0.85<BR>\n" );
document.write( "P(B|A) = 0.05882<BR>\n" );
document.write( "P(B|A) = 0.059\r<BR>\n" );
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document.write( "Answer: 0.059<BR>\n" );
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