document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=625534>Question 625534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. If you flip a fair coin five times in a row, what is the probability that you will have an outcome that has exactly four heads?<BR>\n" );
document.write( " 2. If you flip a fair coin five times in a row, what is the probability that you will have an outcome that has three or more heads?<BR>\n" );
document.write( " 3. If you flip a fair coin five times in a row, what is the probability that you will have an outcome that has two or fewer heads?<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 #393605 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x denote the number of heads.\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P(x = 4) = {{5}\choose{4}} (\frac{1}{2})^5 = \frac{5}{32}\">\r<BR>\n" );
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document.write( "2. and 3. are pretty easy. By symmetry, P(x = 3) = P(x = 2) because the probability of obtaining a head and a tail is the same. Similarly, P(x = 4) = P(x = 1) and P(x = 5) = P(x = 0).\r<BR>\n" );
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document.write( "Therefore, without doing any calculations, we can say that P(x >= 3) and P(x <= 2) are both equal, and they are equal to 1/2. </SPAN>\n" );
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