Question

A coffee franchise is opening a new store. The company estimates that there is an 80% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 10% chance the store will lose $4,000. Determine the expectedgain or loss for this store.The expected value is

Answer 1

If P(x) is the probability of the store having a gain or loss with value x, we have:

P(45000) = 0.80

P(0) = 0.1

P(-4000) = 0.1

Therefore, the expected gain of loss for this store is given by:

`\begin{gathered} \langle x\rangle=45000\cdot P(45000)+0\cdot P(0)-4000\cdot P(4000) \\ \langle x\rangle=36000-400 \\ \langle x\rangle=\text{ \$35,600} \end{gathered}`