document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032915>Question 1032915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you flip a \"strange\" coin twice, where the probability of two heads and two tails are the same (P(HH)=P(TT))  and the probability of one head and one tail is the same in either order (P(HT)=P(TH))  but the probability of HH  is 7 times the probability of HT . <BR>\n" );
document.write( " a)   Find the probability of two heads. <BR>\n" );
document.write( "P(HH)=    <BR>\n" );
document.write( " b)   Let A  be the event that at least one of the coin flips is a head. What is P(A) ? <BR>\n" );
document.write( "P(A)=   <BR>\n" );
document.write( " c)   Let B  be the event that the two flips match. What is P(B) ? <BR>\n" );
document.write( "P(B)=    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647905 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=647905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(HH) = P(TT) = x<BR>\n" );
document.write( "P(HT) = P(TH) = x/7 (since P(HH) = 7*P(HT))\r<BR>\n" );
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document.write( "Since HH, TT, HT, TH are disjoint and one of these outcomes must occur, the sum of their probabilities is 1. Hence x + x + (x/7) + (x/7) = 1, or x = 7/16.\r<BR>\n" );
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document.write( "a) P(HH) = x = 7/16<BR>\n" );
document.write( "b) P(A) = 1 - P(TT) = 9/16<BR>\n" );
document.write( "c) P(B) = P(HH) + P(TT) = 7/8 </SPAN>\n" );
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