document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117538>Question 1117538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I have a question! I tried the first one on my own and I think it's correct.Any help is greatly appreciated! Thank you so much! It helps me out a lot!\r<BR>\n" );
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document.write( "It's a two part question:\r<BR>\n" );
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document.write( "I flip a coin 3 times and get all heads. \r<BR>\n" );
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document.write( "1. Does that mean the next has got to be tails? Why or why not. I said no, because the next time you flip, it could be heads again. \r<BR>\n" );
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document.write( "2. In the long run, what proportion of flips will up as heads? This is where I am stuck. Again any help is greatly appreciated and welcomed! Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732642 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=732642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Your answer to part 1 is absolutely correct.  If you flip a (fair) coin 99 times and get a head each time, the probability of a tail on the 100 flip is still one-half, exactly what the probability was on each of the preceding flips.\r<BR>\n" );
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document.write( "With a fair coin, as in one that doesn't have a drop of solder on it to make one side a little heavier, the probability of a specific outcome, let's say a head, on any given trial is one-half.  You have one outcome that you call a success out of two possible outcomes.  Since either outcome is equally likely (c.f. \"fair coin\"), the long run expectation is getting a head half of the time and a tail the other half.\r<BR>\n" );
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document.write( "However, do not confuse the concept of \"expected outcome\" with \"predicting a future outcome\".  Every trial is completely independent of any previous trial or trials.\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" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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