Question

A contest at a fast food restaurant offered cash prizes and probabilities of winning on one visit. Suppose we spend 1 dollar to buy a pass that let us go to 15 different restaurants in the chain and pick up entry forms. What is the expected value?

Answer 1

We have to calculate the expected value (or the expected prize) when we buy a $1 pass for 15 different restaurants.

This means that we expect 15 times the expected prize of one restaurant.

We then can start by calculating the expected prize for visiting one restaurant using the table.

The expected value of the prize is equal to the sum of the products of each of the prizes and their probabilities.

Then, we can write:

`\begin{gathered} E(x)=\sum ^5_(i\mathop=5)p_i\cdot x_i \\ E(x)=(1)/(125430150)\cdot75000+(1)/(26400540)\cdot20000+(1)/(825450)\cdot3000+(1)/(25480)\cdot150+(1)/(560)\cdot1 \\ E(x)\approx0.000598+0.000758+0.003634+0.005887+0.001786 \\ E(x)\approx0.012663 \end{gathered}`

The expected prize per visit is approximately $0.012663.

Then, if we have 15 visits, we can estimate the expected prize of the 15 visits as:

`E(15\cdot x)=15\cdot E(x)=15\cdot0.012663\approx0.19`