document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315863>Question 315863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jelly bean is red.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the probability that it came from the first bag?\r<BR>\n" );
document.write( "\n" );
document.write( "(Bayes's theorem) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225987 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=225987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jelly bean is red. <BR>\n" );
document.write( "What is the probability that it came from the first bag? <BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "P(1st|red) = P(1st and red)/P(red)<BR>\n" );
document.write( "= [P(red|1st)*P(1st)]/[P(red and 1st + P(red and 2nd)]<BR>\n" );
document.write( "= [(4/6)*(1/2)]/[(4/6)*(1/2) + (2/5)(1/2)]<BR>\n" );
document.write( "= [(1/3)/[(1/3)+(1/5)]<BR>\n" );
document.write( "= (1/3)/(8/15)<BR>\n" );
document.write( "= 5/8<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );