document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114823>Question 1114823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the game of tennis, first serves are distinct from second serves in that the player will generaly take a more powerful swing (bigger chance for error) on the first serve, since he/she is always allowed a second serve if the first lands out of bounds. Suppose a tennis player makes a successful first serve 46% of the time, and she will serve 20 first serves in a row.\r<BR>\n" );
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document.write( "a. If we assume that each serve is independent of the others, why does the number of successful first serves follow a binomial process? Justify your answer.\r<BR>\n" );
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document.write( "b. Let X = the number of successful first serves. Write a probability that she makes at least 7 successful first serves in terms of X, and find the probability.\r<BR>\n" );
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document.write( "c. What is this players average number of first serves in, if she served many sets of 20 first serves? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729749 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=729749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) either the first serve is successful(in the box) or it is not - this is binomial probability.<BR>\n" );
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document.write( "b) the general form of the binomial probability formula is<BR>\n" );
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document.write( "Probability (P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where p is the probability of success, nCk = n!/(k! * (n-k)!)<BR>\n" );
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document.write( "P (at least 7 successful serves out of 20) = summation of k = 7 to 20 of P(k successes in 20 trials) 20Ck * 0.46^k * (1-0.46)^(20-k) = 0.888 approximately 0.89<BR>\n" );
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document.write( "c) players average is 0.46 * 20 = 9.2 approximately 9<BR>\n" );
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