document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175661>Question 175661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Diana has a box containing 6 blue, 8 red, 5 purple, 9 green, and 2 clear marbles that are all the same size and shape.  What is the probability of randomly choosing a clear marble on the first pick; replacing it, and then randomly choosing a purple marble on the second pick? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130770 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=130770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6 blue<BR>\n" );
document.write( "8 red<BR>\n" );
document.write( "5 purple<BR>\n" );
document.write( "9 green<BR>\n" );
document.write( "2 clear<BR>\n" );
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document.write( "30 total<BR>\n" );
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document.write( "probability of getting a clear marble on the first pick is 2/30 because there are 2 clear marbles out of a total of 30 marbles in the box.<BR>\n" );
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document.write( "probability of getting a purple marble on the second pick regardless of what was chosen on the first pick is 5/30 because there are 5 purple marbles out of a total of 30 marbles in the box once again since you put the marble you took on the first pick back in the box.<BR>\n" );
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document.write( "the probability of getting a clear marble on the first pick, putting it in the box, and then getting a purple marble on the second pick is 2/30 * 5/30.<BR>\n" );
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document.write( "if the probability of an event happening is x, and the probability of another event happening is y, then the probability of both events happening is x*y.<BR>\n" );
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document.write( "by replacing the clear marble in the box, you made the two individual events independent of each other.  if you did NOT replace the clear marble, then the probability of getting a purple marble on the second pick would have changed.<BR>\n" );
document.write( "in that case it would have been 5/29 rather than 5/30.<BR>\n" );
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