Answer to Question #182139 in Statistics and Probability for Macinia Lopez

Question #182139

. A lottery ticket pays off 300,000,000 pesos is made available for 10,000,000 tickets. Each ticket costs 50 pesos. Supposed the variable X gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket?


1
Expert's answer
2021-05-04T11:28:35-0400

The probability that the ticket is winning (net winnings are equal to 300000000-50 = 299999950) is "{p_1} = \\frac{1}{{10000000}}"

The probability that a ticket without a win (net win is -50) is "{p_2} = \\frac{{10000000 - 1}}{{10000000}} = \\frac{{{\\rm{9999999}}}}{{10000000}}"

We have a distribution series

"\\begin{matrix}\n{{x_i}}&{299999950}&{ - 50}\\\\\n{{p_i}}&{\\frac{1}{{10000000}}}&{\\frac{{{\\rm{9999999}}}}{{10000000}}}\n\\end{matrix}"

Then the expected gain is

"M(x) = \\sum {{x_i}{p_i}} = \\frac{{299999950 \\cdot 1 - 50 \\cdot {\\rm{9999999}}}}{{10000000}} = -20"

Answer: -20 pesos


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