Question

The women's organization of barangay Ouano, organize a raffle draw. The members aim to sell 1,000 raffle tickets at Php 50 per ticket and each ticket has an equal chance of winning. The prizes are follows: 1st prize-24 inches Sony LED TV worth Php 10,000, 2nd prize-washing machine worth Php 5,000 and 3rd prize-grocery pack worth Php 2,500. Let X denote the net gain from the purchase of one ticket. Find the expected value of X, then interpret.

Answer 1

$P\left( X=10000-50 \right) =\frac{1}{1000}\\P\left( X=5000-50 \right) =\frac{1}{1000}\\P\left( X=2500-50 \right) =\frac{1}{1000}\\P\left( X=-50 \right) =\frac{997}{1000}\\EX=\frac{1}{1000}\left( 1000-50 \right) +\frac{1}{1000}\left( 5000-50 \right) +\frac{1}{1000}\left( 2500-50 \right) +\frac{997}{1000}\cdot \left( -50 \right) =-41.5\\The\,\,gain\,\,is\,\,negative \,because\,\,the\,\,organization\,\,wins\,\,and\,\,people\,\,lose\,\,money.$