document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165446>Question 1165446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary bakes 8 chocolate chip cookies and 10 peanut butter cookies. Bill bakes 5 chocolate chip cookies and 10 peanut butter cookies. The 33 cookies are put together and offered on a single plate. I pick a cookie at random from the plate.<BR>\n" );
document.write( "(a) What is the probability that the cookie is chocolate chip? <BR>\n" );
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document.write( "(b) What is the probability that Mary baked the cookie? <BR>\n" );
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document.write( "(c) What is the probability that the cookie is chocolate chip given that Mary baked it? <BR>\n" );
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document.write( "(d) Use Bayes's theorem to calculate the probability that the cookie is baked by Mary given that it is chocolate chip. In this situation, Bayes's theorem tells us that<BR>\n" );
document.write( "P(Mary given Chocolate) =  P(Chocolate given Mary) × P(Mary)\r<BR>\n" );
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document.write( "                                                               P(Chocolate)<BR>\n" );
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document.write( "(e) Calculate without using Bayes's theorem the probability that the cookie is baked by Mary given that it is chocolate chip. Suggestion: How many of the chocolate chip cookies were baked by Mary? <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 #789941 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 13 C<BR>\n" );
document.write( "20 PB \r<BR>\n" );
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document.write( "a. 13/33 probability <BR>\n" );
document.write( "b. 18/33 or 6/11<BR>\n" );
document.write( "c. 8/18 or 4/9 <BR>\n" );
document.write( "d. P(M|C)=8/13<BR>\n" );
document.write( "=P(C|M)=4/9 <BR>\n" );
document.write( "P(M)=6/11<BR>\n" );
document.write( "P(C)=13/33<BR>\n" );
document.write( "4/9*6/11 divided by 13/33<BR>\n" );
document.write( "that is (24/99)divided by 13/33<BR>\n" );
document.write( "or 8/33 divided by 13/33<BR>\n" );
document.write( "which is 8/13, which is what was described above and is what is wanted for e.\r<BR>\n" );
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