document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59039>Question 59039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A construction company has submitted bids on two separate state contracts, A and B. The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B. Furthermore, the company believes that it has an 80% chance of winning contract A given that it wins contract B.\r<BR>\n" );
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document.write( "a)	What is the probability that the company will win both contracts?\r<BR>\n" );
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document.write( "b)	What is the probability that the company will win at least one of the two contracts?\r<BR>\n" );
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document.write( "c)	If the company wins contract B, what is the probability that it will not win contract A?\r<BR>\n" );
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document.write( "d)	What is the probability that the company will win at most one of the two contracts?\r<BR>\n" );
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document.write( "e)	What is the probability that the company will win neither contract?<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 #40484 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=40484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B. Furthermore, the company believes that it has an 80% chance of winning contract A given that it wins contract B.<BR>\n" );
document.write( "P(A)=0.6; P(not A)=0.4<BR>\n" );
document.write( "P(B)=0.5; P(not B)=0.5<BR>\n" );
document.write( "P(A|B)=0.8; P(not A|B)=0.2<BR>\n" );
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document.write( "a) What is the probability that the company will win both contracts? <BR>\n" );
document.write( "P(A and B)= P(A|B)*P(B)=0.8*0.5=0.4<BR>\n" );
document.write( "Comment: <BR>\n" );
document.write( "Notice that P(A and B) is not equal to P(A)*P(B)<BR>\n" );
document.write( "because 0.4 is not equal to 0.6*0.5=0.3<BR>\n" );
document.write( "Therefore events A and B are dependent.\r<BR>\n" );
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document.write( "b) What is the probability that the company will win at least one of the two contracts?<BR>\n" );
document.write( "P(at least one)= 1 - P(win none)= 1- 0.4*0.5=0.8 \r<BR>\n" );
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document.write( "c) If the company wins contract B, what is the probability that it will not win contract A? <BR>\n" );
document.write( "P(notA |B)= P(not A and B)/P(B) = 0.4*0.5/0.5 = 0.4\r<BR>\n" );
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document.write( "d) What is the probability that the company will win at most one of the two contracts? <BR>\n" );
document.write( "P(at most one) = 1 - P(both)= 1-0.4 = 0.6\r<BR>\n" );
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document.write( "e) What is the probability that the company will win neither contract?<BR>\n" );
document.write( "P(not A and notB)=0.4*0.5 = 0.2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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