Question

The college student senate is sponsoring a spring break Caribbean cruise raffle, with proceeds going to the local homeless shelter. A local travel agency donated the cruise, worth an estimated $3000. The students sold 2900 tickets at $5 per ticket. Find the mathematical expectation of a student who purchases 10 tickets.

Answer 1

The mathematical expectation of a student who purchases 10 tickets is -$39.65.

Explanation:

A student that purchases 10 tickets out of 2900 has a probability of winning the cruise that can be calculated as:

`p=10/2900\approx0.00345`

Each ticket cost $5, so he has spent $50 for the 10 tickets.

Then, the expected value of this operation is equal to the expected value of the earnings (probability of winning the prize multiplied by the value of the prize), minus the costs:

`E(X)=p\cdot R-C\\\\E(X)=0.00345\cdot3000-50=10.35-50=-39.65`

The mathematical expectation of a student who purchases 10 tickets is -$39.65.