document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86612>Question 86612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can someone help me with these problems when you have a few min. thanks.\r<BR>\n" );
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document.write( "Problem #1<BR>\n" );
document.write( "Suppose you have three jars with the following contents: 2 black balls and 1 white ball in the first, 1 black ball and 2 white balls in the second, and 1 black ball and 1 white ball in the third. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. If<BR>\n" );
document.write( "the probabilities of selecting the first, second, or third jar are 1/ 2, 1/ 3, and 1 /6, respectively,find the probabilities that if a white ball is drawn, it came from the following jars.\r<BR>\n" );
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document.write( "A) The third jar\r<BR>\n" );
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document.write( "Problem #2<BR>\n" );
document.write( "Laura Johnson, a game show contestant, could win one of two prizes: a shiny new<BR>\n" );
document.write( "Porsche or a shiny new penny. Laura is given two boxes of marbles. The first box has<BR>\n" );
document.write( "50 pink marbles in it and the second box has 50 blue marbles in it. The game show<BR>\n" );
document.write( "host will pick someone from the audience to be blindfolded and then draw a marble<BR>\n" );
document.write( "from one of the two boxes. If a pink marble is drawn, she wins the Porsche. Otherwise,<BR>\n" );
document.write( "Laura wins the penny.* Can Laura increase her chances of winning by redistributing<BR>\n" );
document.write( "some of the marbles from one box to the other? Explain.\r<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 #62678 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=62678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1st Problem:\r<BR>\n" );
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document.write( "p(3rd jar|white)<BR>\n" );
document.write( "=[P(3rd jar and white)/P(w)<BR>\n" );
document.write( "=[(1/6)*(1/2)]/]P(white and 1st)+P(white and 2nd)+P(white and 3rd)]<BR>\n" );
document.write( "=[1/12]/[(1/2)(1/4)+(1/3)(2/3)+(1/6)(1/2)]<BR>\n" );
document.write( "= [1/12]/[31/72] <BR>\n" );
document.write( "= 6/31<BR>\n" );
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document.write( "2nd Problem:\r<BR>\n" );
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document.write( "As it stands her chances of winning are 1/2<BR>\n" );
document.write( "If she changes the mixture to Jar1 with x pink and 50-x white and Jar2 with 50-x pink  and and x white, the probability of pink is still <BR>\n" );
document.write( "(1/2)(x/50) + 1/2(50-x)/50<BR>\n" );
document.write( "= (1/2)[x/50 + (50-x)/50]<BR>\n" );
document.write( "= 1/2 [ (50x+2500-50x)/2500] = (1/2)(1) = 1/2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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