document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164736>Question 1164736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the following probabilities and indicate which probability distribution model is<BR>\n" );
document.write( "appropriate in each case. A very good darts player can hit the bull’s eye (red circle in the<BR>\n" );
document.write( "center of the dart board) 65% of the time. What is the probability that he<BR>\n" );
document.write( "(a) hits the bull’s eye for the 10th time on the 15th try?<BR>\n" );
document.write( "(b) hits the bull’s eye 10 times in 15 tries?<BR>\n" );
document.write( "(c) hits the first bull’s eye on the third try?<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 #789142 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Two things:\r<BR>\n" );
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document.write( "1. If the probability of success for any given trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\">, then the probability of failure for any given trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1\ -\ p\">.\r<BR>\n" );
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document.write( "2. The probability of exactly <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials where the probability of success on any given trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(k,n,p)\ =\ {{n}\choose{k}}\,(p)^k(1-p)^{n-k}\">\r<BR>\n" );
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document.write( "For part a) you need the probability of 9 successes in 14 trials times the probability of success once, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \(P(9,14,0.65)\)(p)\ =\ \({{14}\choose{9}}\,(0.65)^9(0.35)^{5}\)(p)\">\r<BR>\n" );
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document.write( "For part b) it is just <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(10,15,0.65)\">\r<BR>\n" );
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document.write( "And for part c) you need the probability of missing on the first two tries times the probability of hitting once, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \(P(2,2,0.35)\)(p)\">\r<BR>\n" );
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document.write( "You can do your own arithmetic\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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