document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=745392>Question 745392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability of C is 0.25. The conditional probability that C occurs given that D occurs is 0.3. The conditional probability that C occurs given that D does not occur is 0.2. \r<BR>\n" );
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document.write( "(a) What is the probability that D occurs?\r<BR>\n" );
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document.write( "(b) What is the conditional probability that D occurs given that C occurs?<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 #453917 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=453917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of C is 0.25. The conditional probability that C occurs given that D occurs is 0.3. The conditional probability that C occurs given that D does not occur is 0.2. <BR>\n" );
document.write( "(a) What is the probability that D occurs?<BR>\n" );
document.write( "P(C and D) = 0.3*P(D)<BR>\n" );
document.write( "P(C and D') = 0.2*P(D')<BR>\n" );
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document.write( "Add to get:<BR>\n" );
document.write( "P(C) = 0.3P(D) + 0.2(1-P(D))<BR>\n" );
document.write( "0.25 = 0.3P(D) + 0.2 - 0.2P(D)<BR>\n" );
document.write( "0.05 = 0.1P(D)<BR>\n" );
document.write( "P(D) = 0.5<BR>\n" );
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document.write( "(b) What is the conditional probability that D occurs given that C occurs?<BR>\n" );
document.write( "P(D | C) = P(C and D)/P(C)<BR>\n" );
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document.write( "P(C and D) = 0.3*P(D) = 0.3*0.5 = 0.15<BR>\n" );
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document.write( "So, P(D | C) = 0.15/0.25 = 3/5 = 0.6<BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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