A company makes cellular phones. One out of every $25$ phones are faulty, but the company doesn’t know which phones are faulty until a customer complains. Suppose the company makes a $ \$ 30$ profit on the sale of any working phone but loses $ \$ 800$ for every faulty phone because they must replace it.
I have this shown below, however, I am getting a negative number:
$$E(x)= \frac{24}{25} \cdot 30 + \frac{1}{25} \cdot-800$$
There's nothing wrong with what you have done.
Take a simpler problem for example: calculate the expected value if I gain $1$ dollar for a head, and lose $2$ dollars for a tail. I am losing money on average, so how does the expected value tell me I am losing money?