document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162755>Question 1162755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Questions are based on the following information: The fine print on an instant lottery ticket claims that one in nine tickets win a prize.\r<BR>\n" );
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document.write( "What is the probability that you win at least once if you purchase five tickets?<BR>\n" );
document.write( "What is the probability that you win at least twice if you purchase ten tickets?<BR>\n" );
document.write( "What is the approximate probability that you win more than 120 times if you purchase 900 tickets?<BR>\n" );
document.write( "Of all awarded prizes, 10% are worth Ghc1000, 20% are worth Ghc100, and 70% are worth $10. Find the expected winnings if you purchase a single ticket. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786600 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=786600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probability you don't win is 8/9 each time<BR>\n" );
document.write( "for 5 times NOT winning at all, the probability is (8/9)^5=0.5549<BR>\n" );
document.write( "all other possibilities are winning at least once, and that is 1-0.5549=0.4451\r<BR>\n" );
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document.write( "For 10 tickets, probability don't win is (8/9)^10=0.3079<BR>\n" );
document.write( "probability win 1 time is 10*(8/9)^9*(1/9), because 10 ways can win once<BR>\n" );
document.write( "That probability is 0.3849<BR>\n" );
document.write( "Those two sum to 0.6929<BR>\n" );
document.write( "All other probabilities are winning at least 2 or more times, and that is 1-0.6929=0.3071\r<BR>\n" );
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document.write( "np=900*(1/9)=100 times<BR>\n" );
document.write( "variance is np(1-p)=100*(8/9)=88.89<BR>\n" );
document.write( "sd is sqrt (V)=9.43<BR>\n" );
document.write( "normal approximation is  z>(120-100)/9.43 or z>2.12, and that probability is 0.0170.\r<BR>\n" );
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document.write( "E(X)=(1/9)(0.1*1000+0.2*100+0.7*10)<BR>\n" );
document.write( "=(1/9)(127)<BR>\n" );
document.write( "=Ghc14.11; I am ignoring the dollar sign for the last prize.<BR>\n" );
document.write( "This is the expected value for the winnings. The overall expected value cannot be determined, since the price of the tickets is not unknown. That would be subtracting (8/9)*price of the ticket from the above figure. </SPAN>\n" );
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