document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192893>Question 1192893</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An unfair coin has probability p of landing heads up on a single flip, where<BR>\n" );
document.write( "0 < p < 1. The coin is tossed seven times, and the probability that the coin lands<BR>\n" );
document.write( "heads up exactly twice is equal to the probability that the coin lands heads up<BR>\n" );
document.write( "exactly three times. What is the value of p? Express your answer as a common<BR>\n" );
document.write( "fraction.\r<BR>\n" );
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document.write( "Can I get help on this please? Trying to understand how to solve this? Thank you for your help and time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824822 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=824822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The probability of heads is p; the probability of tails is (1-p).<br><BR>\n" );
document.write( "The probability of getting 2 heads on 7 flips is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%287%2C2%29%28%28p%29%5E2%29%28%28p-1%29%5E5%29 ALIGN=MIDDLE  ALT=\"C%287%2C2%29%28%28p%29%5E2%29%28%28p-1%29%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The probability of getting 3 heads on 7 flips is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%287%2C3%29%28%28p%29%5E3%29%28%28p-1%29%5E4%29 ALIGN=MIDDLE  ALT=\"C%287%2C3%29%28%28p%29%5E3%29%28%28p-1%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The probabilities of 2 or 3 heads are the same:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%287%2C2%29%28%28p%29%5E2%29%28%281-p%29%5E5%29=C%287%2C3%29%28%28p%29%5E3%29%28%281-p%29%5E4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%28%28p%29%5E2%29%28%281-p%29%5E5%29=35%28%28p%29%5E3%29%28%281-p%29%5E4%29 ALIGN=MIDDLE  ALT=\"21%28%28p%29%5E2%29%28%281-p%29%5E5%29=35%28%28p%29%5E3%29%28%281-p%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%281-p%29=35%28p%29 ALIGN=MIDDLE  ALT=\"21%281-p%29=35%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21-21p=35p ALIGN=MIDDLE  ALT=\"21-21p=35p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21=56p ALIGN=MIDDLE  ALT=\"21=56p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=21%2F56+=+3%2F8 ALIGN=MIDDLE  ALT=\"p=21%2F56+=+3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: p=3/8<br><BR>\n" );
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