document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197108>Question 1197108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Robert bought a $2 lottery ticket such that 1 in 100 would win $9, 1 in 1000 would win $80, and 1 in 50 million would win 1 million. What is the expected value of a lottery ticket in dollars?\r<BR>\n" );
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document.write( "Does Robert expect to earn a profit if he buys 100 tickets?\r<BR>\n" );
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document.write( "Select an answer<BR>\n" );
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document.write( "By how much? </SPAN>\n" );
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document.write( "1 in 100 = 1/100 = 0.01<BR>\n" );
document.write( "1 in 1000 = 1/1000 = 0.001<BR>\n" );
document.write( "1 in 50 million = 1/(50 million) = 1/(50*10^6) = 0.00000002\r<BR>\n" );
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document.write( "Those probability values add to:<BR>\n" );
document.write( "0.01+0.001+0.00000002 = 0.01100002<BR>\n" );
document.write( "Subtract that from 1<BR>\n" );
document.write( "1-0.01100002 = 0.98899998<BR>\n" );
document.write( "This represents the probability of winning $0\r<BR>\n" );
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document.write( "X = net winnings = (amount won) - ($2 cost)<BR>\n" );
document.write( "P(X) = probability of getting those net winnings<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >P(X)</TD><TD >X*P(X)</TD></tr><tr><TD >7</TD><TD >0.01</TD><TD >0.07</TD></tr><tr><TD >78</TD><TD >0.001</TD><TD >0.078</TD></tr><tr><TD >999998</TD><TD >0.00000002</TD><TD >0.01999996</TD></tr><tr><TD >-2</TD><TD >0.98899998</TD><TD >-1.97799996</TD></tr>\n" );
document.write( "</TABLE>Add up the values in the X*P(X) column<BR>\n" );
document.write( "0.07 + 0.078 + 0.01999996 + (-1.97799996) = -1.81\r<BR>\n" );
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document.write( "The expected earnings for each lottery ticket, on average, is -1.81 dollars.<BR>\n" );
document.write( "This means Robert expects to lose on average about $1.81 per ticket.\r<BR>\n" );
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document.write( "It doesn't matter how many tickets he buys. He won't earn a profit since the profit per ticket is negative.<BR>\n" );
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