An inspector at a manufacturing plant examines boxes containing table lamps that are ready for shipment. Some of the boxes are slightly damaged, and he knows that the lamp inside such a box has a $20\%$ chance of being broken. Shipping a broken lamp to a customer generates a $$20$ cost due to replacement costs and customer dissatisfaction. On the other hand, the inspector may open the box now.

If he does, he'll find the lamp either broken or unbroken. If the lamp is broken it is discarded, and replacing and repackaging the new lamp costs the company $$10.$ If it is unbroken, it is repackaged at a cost of $$1,$ then shipped.

Suppose that the inspector sees a slightly damaged box and decides to open it to see if the lamp inside it is broken. On average, how much of a cost will be incurred by the company by this course of action with this damaged box? Give your answers in dollars, but do not include the dollar sign. For example $$15\mathrm{.}30$ would be entered as $15\mathrm{.}30$ or $15\mathrm{.}3.$