document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077068>Question 1077068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability that Sam will win in a certain game whenever he plays is 2/5. If he plays two games, what is the probability that he will win just the first game? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691720 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=691720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = 2/5<BR>\n" );
document.write( "q = 1 - 2/5 = 3/5\r<BR>\n" );
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document.write( "probability he wins any game he plays in is 2/5<BR>\n" );
document.write( "probability he loses any game he plays in is 3/5\r<BR>\n" );
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document.write( "he plays 2 games.\r<BR>\n" );
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document.write( "probability he wins the first game only is 2/5 * 3/5 = 6/25\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "probability he wins the second game only is 3/5 * 2/5 = 6/25\r<BR>\n" );
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document.write( "probability he wins both games is 2/5 * 2/5 = 4/25\r<BR>\n" );
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document.write( "probability he loses both games is 3/5 * 3/5 = 9/25\r<BR>\n" );
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document.write( "sum of all probabilities must be equal to 1.\r<BR>\n" );
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document.write( "6/25 + 6/25 + 4/25 + 9/25 = 25/25 = 1\r<BR>\n" );
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document.write( "everything checks out.\r<BR>\n" );
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document.write( "probability he wins the first game only is 6/25.\r<BR>\n" );
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