document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165680>Question 1165680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A basketball player hits her free throws 80% of the time.<BR>\n" );
document.write( "(a) Find the probability she misses for the second time on her 10th attempt.<BR>\n" );
document.write( "(b) If she shoots 20 free throws, what is the probability she makes at least 19 of them?<BR>\n" );
document.write( "(c) Assume that offensive fouls are equally likely to occur at any time during a game, and on<BR>\n" );
document.write( "average 6 offensive fouls occur in a game. What is the probability of at least 8 offensive fouls occur in a<BR>\n" );
document.write( "game.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790238 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Probability misses once in first 9 times is 9*0.8^8*0.2, the binomial formula. That is 0.3020.<BR>\n" );
document.write( "The miss on the 10th has probability 0.2. That is multiplied by the first value to get 0.0604, the answer, assuming independence, which allows us to multiply these.\r<BR>\n" );
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document.write( "making all 20 is probability 0.8^20, or 0.0115.<BR>\n" );
document.write( "making 19 is 20*0.8^19*0.2=0.0576<BR>\n" );
document.write( "that sum is 0.0691\r<BR>\n" );
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document.write( "The last is Poisson, since no fixed trials, proportional to time and theoretically could be infinite. From the calculator, 7 or fewer has probability 0.7440, so the answer is the complement of 0.2560. It is more difficult doing it by hand from 8 on because need to do many more calculations until the value is insignificant, which is around P(15).\r<BR>\n" );
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document.write( "0.2560\r<BR>\n" );
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