document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197528>Question 1197528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An experiment consists of tossing 5 fair​ (not weighted)​ coins, except one of the  coins has 5 a head on both sides. Compute the probability of obtaining exactly  2 heads. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830831 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=830831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The wording is a bit confusing, but it sounds like there are 5 fair coins, and there's an extra 6th special coin which has 2 heads.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since that special coin has 2 heads, this means we are guaranteed at least one head in the 6 coins. <BR>\n" );
document.write( "We just need to find the probability of getting exactly 1 head in the five fair coins.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll use the binomial distribution. <BR>\n" );
document.write( "n = 5 coins<BR>\n" );
document.write( "x = 1 head exactly is what we're after<BR>\n" );
document.write( "p = 0.5 is the probability of getting heads<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%28x%29+=+expr%28%28n%21%29%2F%28x%21%2A%28n-x%29%21%29%29%2A%28p%5Ex%29%2A%281-p%29%5E%28n-x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%28x%29+=+expr%28%285%21%29%2F%28x%21%2A%285-x%29%21%29%29%2A%280.5%5Ex%29%2A%281-0.5%29%5E%285-x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%281%29+=+expr%28%285%21%29%2F%281%21%2A%285-1%29%21%29%29%2A%280.5%5E1%29%2A%281-0.5%29%5E%285-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%281%29+=+5%2A%280.5%5E1%29%2A%281-0.5%29%5E%285-1%29 ALIGN=MIDDLE  ALT=\"B%281%29+=+5%2A%280.5%5E1%29%2A%281-0.5%29%5E%285-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%281%29+=+0.15625 ALIGN=MIDDLE  ALT=\"B%281%29+=+0.15625\"   DISABLED_style= \"max-width:90%; height:auto;\" > This value is exact\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The 0.5^1 portion represents the probability of getting that 1 head<BR>\n" );
document.write( "(1-0.5)^(5-1) represents the probability of getting 4 tails<BR>\n" );
document.write( "The 5 out front is the number of ways to get 1 head, ie <BR>\n" );
document.write( "HTTTT<BR>\n" );
document.write( "THTTT<BR>\n" );
document.write( "TTHTT<BR>\n" );
document.write( "TTTHT<BR>\n" );
document.write( "TTTTH\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red>0.15625</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );