Answer to Question #321008 in Statistics and Probability for Rome

Question

2. A company holds a raffle game. The amount to be won are as follows: one Php10, 000; two Php5, 000 each and four Php2, 000 each. Two thousand tickets were sold at Php100 each. If you buy one of the raffle tickets, what is your expected net gain?

Answer 1

Let X - our net gain. It may be any value of 9900, 4900, 1900, -100.

If we won 10000 Php, our net gain is 10000 - 100, because we have bought a ticket, and so on.

The probabilities of these values are:

$P(X=9900)=\cfrac{1}{2000},\\ P(X=4900)=\cfrac{2}{2000},\\ P(X=1900)=\cfrac{4}{2000},\\ P(X=-100)=\cfrac{2000-1-2-4}{2000}=\cfrac{1993}{2000}.$

The expected net gain:

$\mu=\sum x_i\cdot P(X=x_i)=\\ =9900\cdot\cfrac{1}{2000}+4900\cdot\cfrac{2}{2000}+\\ +1900\cdot\cfrac{4}{2000}-100\cdot\cfrac{1993}{2000}=-86.$