document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=334673>Question 334673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag is filled with 16 red marbles and 49 white marbles. With replacement what is the probability of picking a red mable.  I do not understand how to use replacemnet to find the answer.  Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239812 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=239812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Replacement doesn't make any sense in the context of the probability of picking <i>a</i> red marble.  Now if you were interested in the probability of picking a red marble <i>on the second (or subsequent) trial</i>, THEN replacement makes a difference.\r<BR>\n" );
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document.write( "If you are only concerned with the first try, replacement doesn't matter.  The probability is simply the number of red marbles divided by the total number of marbles.\r<BR>\n" );
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document.write( "But if you want the probability of picking a red one on the second try, you have  to consider whether the one you picked in the first place 1. was red or not, and 2. went back in the bag.\r<BR>\n" );
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document.write( "Here's the deal.  The probability of picking a red marble on the first go is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{16}{60}\ =\ \frac{4}{15}\">.  Now if you put the marble back in the bag, the probability of picking a red one on the second go is exactly the same, because you have the same total number of marbles and the same number of red marbles.  BUT, if you DON'T put the first one chosen back in the bag, then things change.\r<BR>\n" );
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document.write( "In this case, if the first marble chosen was white, then you would have 16 red marbles and 48 white marbles left in the bag for the second draw and the probability would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{16}{59}\">.  But if the first one was red, then the probability of picking a second red one is now <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{15}{59}\">\r<BR>\n" );
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document.write( "See?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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