document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=558903>Question 558903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> player 1 chooses a number between 1 and 10. Then player 2 chooses a number between 1 and 10. What is the   probability of player 2 choosing a higher number than player 1?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363390 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=363390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let N1 and N2 be the numbers chosen by players 1 and 2.\r<BR>\n" );
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document.write( "Note that we have three probabilities: P(N2 > N1), P(N1 > N2) and P(N1 = N2). Exactly one of these happens, so the sum of these three probabilities is 1.\r<BR>\n" );
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document.write( "By symmetry, we can say that P(N2 > N1) = P(N1 > N2) because the players' numbers are independent of each other, and {N1, N2} = {9,4} and {N1, N2} = {4,9} have the same probability of occurring, for example.\r<BR>\n" );
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document.write( "To find P(N1 = N2), simply fix N1 (e.g. suppose N1 = 6). Then P(N1 = N2) = 1/10 (one number out of ten is equal to P1).\r<BR>\n" );
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document.write( "Hence we have P(N2 > N1) + P(N1 > N2) + 1/10 = 1 --> P(N2 > N1) + P(N1 > N2) = 9/10. Since these two probabilities are equal, P(N2 > N1) equals half of 9/10, or 9/20.\r<BR>\n" );
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