document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=850137>Question 850137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Was wondering if someone could give me the probability and the equation to solve the following.\r<BR>\n" );
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document.write( "Two teams are to play four games against each other. In each game Team A is 45% to win and team B is 55% to win. What it the probability of Team A winning 2 or more of the games (i.e. 2,3 or 4)? Also if you can show me how to figure it out that would be great.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511979 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the probability of Team A winning 0 or 1 game, then we can subtract from 1.\r<BR>\n" );
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document.write( "p = 0.45 (Team A wins, B loses)<BR>\n" );
document.write( "q = 0.55 (Team B wins, A loses)\r<BR>\n" );
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document.write( "For 0 wins, that would be the probability of 4 wins by team B.<BR>\n" );
document.write( "P(x=0) = q^4<BR>\n" );
document.write( "= (0.55)^4<BR>\n" );
document.write( "= 0.55 * 0.55 * 0.55 * 0.55<BR>\n" );
document.write( "= 0.09150625<BR>\n" );
document.write( "&#8776; 9.15%\r<BR>\n" );
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document.write( "For 1 win, that would be the probability of 1 win by A and 3 wins by B.<BR>\n" );
document.write( "You might think that would just be 0.45 * 0.55 * 0.55 * 0.55, but there are 4 ways to pick which of the matches is won by A.<BR>\n" );
document.write( "P(x=1) = C(4,1) * p^1 * q^3<BR>\n" );
document.write( "= 4 * (0.45) * (0.55)^3<BR>\n" );
document.write( "= 4 * 0.45 * 0.55 * 0.55 * 0.55<BR>\n" );
document.write( "= 0.299475<BR>\n" );
document.write( "&#8776; 29.95%\r<BR>\n" );
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document.write( "P(x=0 or 1) = P(x=0) + P(x=1)<BR>\n" );
document.write( "= 0.0915 + 0.2995<BR>\n" );
document.write( "= 0.3910<BR>\n" );
document.write( "= 39.1%\r<BR>\n" );
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document.write( "But you want the probability of 2 or more which is the opposite probability:<BR>\n" );
document.write( "P(x &#8805; 2) = 1 - P(x = 0 or 1)<BR>\n" );
document.write( "= 1 - 0.3910<BR>\n" );
document.write( "= 0.6090<BR>\n" );
document.write( "= 60.9%\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "P(x &#8805; 2) = 60.9%<BR>\n" );
document.write( " </SPAN>\n" );
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