document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183784>Question 1183784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is randomly drawn from either basket 1 or basket 2.  Basket 1 has 3 white balls and 4 black balls.  Basket 2 has 2 white and 3 black balls. The drawn ball is then randomly put into either basket 3 or basket 4.  Basket 3 has 3 white and 3 black balls.  Basket 4 has 2 white and 4 black balls. A ball is then randomly drawn from either basket 3 or basket 4. \r<BR>\n" );
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document.write( "a) What is the probability of drawing a white ball in the 2nd attempt?<BR>\n" );
document.write( "b) What is the probability of drawing a black ball in the 2nd attempt?<BR>\n" );
document.write( "c) If the 2nd ball drawn is white, what is the probability that it came from basket 4?<BR>\n" );
document.write( "d) If the 2nd ball drawn is black, what is the probability that it came from basket 1?<BR>\n" );
document.write( "e) Which ball draw event is the most likely to happen?  The least likely to happen? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814344 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You will learn nothing, and we will waste a lot of our time, if we work this whole series of related problems for you.  All the concepts involved are basic -- you just need to do the work.<br><BR>\n" );
document.write( "There are 2 choices for which basket to choose first;<BR>\n" );
document.write( "there are 2 choices for the color of ball to choose from that basket;<BR>\n" );
document.write( "there are 2 choices for which basket to put that ball into; and<BR>\n" );
document.write( "there are 2 choices for the color of ball to choose from that second basket<br><BR>\n" );
document.write( "So the number of cases you need to consider is 2*2*2*2=16.<br><BR>\n" );
document.write( "I'll do one of them for you: \"1,B,4,W\" = choose basket 1; select a black from it; put it in basket 4; select a white from basket 4.  The probability is<br><BR>\n" );
document.write( "P(choose basket 1) = 1/2<BR>\n" );
document.write( "P(choose black from basket 1) = 2/5<BR>\n" );
document.write( "P(put the black ball in basket 4) = 1/2<BR>\n" );
document.write( "P(choose a white from basket 4) = 2/7<br><BR>\n" );
document.write( "The probability for this case is then (1/2)(2/5)(1/2)(2/7) = 1/35.<br><BR>\n" );
document.write( "Calculate the probabilities for each of the other 15 cases.  That will give you the answers for parts a, b, and e.<br><BR>\n" );
document.write( "Note you can check your calculations by verifying that the sum of the probabilities for all 16 cases is 1.<br><BR>\n" );
document.write( "For parts c and d, you are dealing with conditional probability. For an example, the answer for part c is<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "      P(2nd ball is white and it was drawn from basket 4)\r\n" );
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document.write( "P(2nd ball is white and it came from either basket 3 or basket 4)</PRE><br><BR>\n" );
document.write( "That calculation will be easy since you will have the probabilities for all 16 cases.<br><BR>\n" );
document.write( " </SPAN>\n" );
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