document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=852124>Question 852124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the probability of a tennis player serving an ace is 1/6, what's the probability that the player will serve 3 aces out of 8 serves?\r<BR>\n" );
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document.write( "I know it's independent probability. I did it like this:<BR>\n" );
document.write( "for \"non-ace\" results, the prob. is 5/6<BR>\n" );
document.write( "for 8 serves, the prob of 3 aces is:\r<BR>\n" );
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document.write( "1/6 * 1/6 * 1/6 * 5/6 * 5/6 * 5/6 * 5/6 * 5/6 = 3125/1,679,616 = approx. 0.00186, or 0.186%, or 186/1000.\r<BR>\n" );
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document.write( "Am I even close? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513169 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=513169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> close but no cigar.<BR>\n" );
document.write( "if you multiply that by the number of possible ways you can get 3 things out of 8 things, then you would be right.<BR>\n" );
document.write( "this, i believe, is a binomial probability type problem.<BR>\n" );
document.write( "the formula for binomial probability is:<BR>\n" );
document.write( "p(x) = nCx * p^x * q^(n-x)<BR>\n" );
document.write( "in your problem:<BR>\n" );
document.write( "n = 8<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "n-x = 5<BR>\n" );
document.write( "p = (1/6)<BR>\n" );
document.write( "q = (5/6)<BR>\n" );
document.write( "using these values, the formula becomes:<BR>\n" );
document.write( "p(3) = 8C3 * (1/6)^3 * (5/6)^5<BR>\n" );
document.write( "8C3 is equal to (8*7*6) / (1*2*3) which is equal to 56.<BR>\n" );
document.write( "(1/6)^3 is equal to .004630<BR>\n" );
document.write( "(5/6)^5 is equal to .401878<BR>\n" );
document.write( ".004630 * .401878 is equal to .001860<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "p(3) = 56 * .004630 * .401878 which is equal to 56 * .001860 which is equal to .104199\r<BR>\n" );
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document.write( "you were close.<BR>\n" );
document.write( "you calculated correctly for one of the possible ways you can get 3 aces out of 8 serves.<BR>\n" );
document.write( "there were 55 more ways to do that.<BR>\n" );
document.write( "i'll just list the first 3 so you can see what i mean.<BR>\n" );
document.write( "let a = probability to get an ace which is equal to 1/6<BR>\n" );
document.write( "let b = probability to not get an ace which is equal to 5/6.<BR>\n" );
document.write( "you showed one way it could happen:<BR>\n" );
document.write( "aaabbbbb<BR>\n" );
document.write( "another way it could happen would be:<BR>\n" );
document.write( "aababbbb<BR>\n" );
document.write( "another way it could happen would be:<BR>\n" );
document.write( "aabbabbb<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "so the probability you calculated is correct but for only one of the ways it could happen.<BR>\n" );
document.write( "there were 55 other ways it could happen as well.\r<BR>\n" );
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document.write( "the binomial probability formula takes that into account.<BR>\n" );
document.write( "p(x) = nCx * p^x * q^(*n-x)<BR>\n" );
document.write( "nCx is the number of possible ways to get x things from n.<BR>\n" );
document.write( "p = probability of the event occurring.<BR>\n" );
document.write( "q k= probability of the event not occurring = 1 - p.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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