document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044198>Question 1044198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lottery ticket claimed that one in nine ticket win a prize.<BR>\n" );
document.write( "a)what is the probability that you win at least twice when you purchase ten tickets<BR>\n" );
document.write( "b)what is the approximate probability that you win more than 120times if you purchase 900 tickets?<BR>\n" );
document.write( "c)Of all awarded prizes,10% are worth $1000,20% are worth %100 and 70% are worth $10.Find the expected winning 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 #659475 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:Lottery ticket claimed that one in nine ticket win a prize.<BR>\n" );
document.write( "a)what is the probability that you win at least twice when you purchase ten tickets<BR>\n" );
document.write( "b)what is the approximate probability that you win more than 120times if you purchase 900 tickets?<BR>\n" );
document.write( "c)Of all awarded prizes,10% are worth $1000,20% are worth %100 and 70% are worth $10.Find the expected winning if you purchase a single ticket.<BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Let X = number of tickets that win a prize<BR>\n" );
document.write( "a) X~Binomial(n = 10, p = 1/9)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X+%3E=+2%29+=+1+-+P%28X+%3C=1%29 ALIGN=MIDDLE  ALT=\"P%28X+%3E=+2%29+=+1+-+P%28X+%3C=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The formula using a TI calculator is <BR>\n" );
document.write( "1-binomcdf(10, 1/9, 1).<BR>\n" );
document.write( "The formula using Excel is<BR>\n" );
document.write( "=1-BINOMDIST(1,10,1/9,TRUE)<BR>\n" );
document.write( "The result to 4 decimal places is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.3071%29 ALIGN=MIDDLE  ALT=\"highlight%280.3071%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) X is approximately normal with mean 900(1/9) = 100 and variance <BR>\n" );
document.write( "900(1/9)(8/9) = 800/9.<BR>\n" );
document.write( "To correct for continuity, subtract 0.5 from X.<BR>\n" );
document.write( "So the desired probability is P(X > 120.5).<BR>\n" );
document.write( "Using a TI calculator, the formula is<BR>\n" );
document.write( "=normalcdf(120.5, 99999, 100, (800/9)^0.5)<BR>\n" );
document.write( "Using Excel, the formula is<BR>\n" );
document.write( "=1-NORMDIST(120.5,100,(800/9)^0.5,TRUE)<BR>\n" );
document.write( "The result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.0148%29 ALIGN=MIDDLE  ALT=\"highlight%280.0148%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) The expected winning is =0.1*1000+0.2*100+0.7*10 = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28127%29 ALIGN=MIDDLE  ALT=\"highlight%28127%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );