Answer to Question #189590 in Statistics and Probability for Gela

Question

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?

Answer 1

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

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

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