# A cash prize of $2,500 is to be awarded at a fundraiser. If 2,500 tickets are sold at $2 each . What is the expected value?

A cash prize of $2,500 is to be awarded at a fundraiser. If 2,500 tickets are sold at $2 each, what is the expected value?

Expected value *E*(*x*) is given by:

E(x)=∑x* P(x), where x gain and P(x) is the probability of gain.

Let’s find the values of x and *P*(*x*):

Win | lose | |

Gain (x) |
2500 – 2 = 2498 | -2 |

Probability P(x) |
1/2500 | 2499/2500 |

Now, the expected value of gain is given by

E(x)=2498∙(1/2500)+(-2)(2499/2500)

=2498/2500-(2∙2499)/2500

=2498/2500-(2∙2499)/2500

=-1

Hence the expected value is -1