document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028126>Question 1028126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One thousand tickets are sold at $1 each. One ticket will be randomly selected and the winner will receive a<BR>\n" );
document.write( "color television valued at $398. What is the expected value for a person that buys one ticket? </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "One thousand tickets are sold at $1 each. One ticket will be randomly selected and the winner will receive a<BR>\n" );
document.write( "color television valued at $398. What is the expected value for a person that buys one ticket?<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Expected value E[x]=&mu; is the overall average value of the game, defined by<BR>\n" );
document.write( "E[x]=&sum; x*P(x) where the summation is taken over all outcomes.<BR>\n" );
document.write( "x=value of an outcome, <BR>\n" );
document.write( "P(x)=probability of that outcome.<BR>\n" );
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document.write( "For the given problem, we have 1000 tickets, out of which one will win a television worth 398. That means 999 people will pay $1 (with a probability of 999/1000 losing) , and the winner will get a value of $398-$1=$397 with a probability of 1/1000 winning).<BR>\n" );
document.write( "Summing over the whole population,<BR>\n" );
document.write( "E[x]=(-1)*999/1000+(397)*1/1000=-602/1000=-0.602 (in dollars) </SPAN>\n" );
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