A Do-It-Yourself Homeowner Is Installing a New Toilet

Essay

A do-it-yourself homeowner is installing a new toilet. While installing the toilet he must decide on what kind of connecting pipe he will install to the water supply. There are two available options, one that has a shut-off valve in case of a leak and a cheaper one without the shut-off valve. Suppose that the shut-off valve pipe costs an extra ten dollars and that the homeowner must buy one of the two.
(a) Draw a decision tree for this scenario, labeling the cost of a leak as X and the chance of a leak as P.
(b) If the chance of a leak causing household damage is 1%, at what $ amount of household damage is the owner neutral on which pipe to buy?
(c) If the cost of a leak would be $10,000 what is the maximum % chance to leak at which the homeowner would prefer to buy the cheaper pipe?
(d) If the cost of a leak is $1,000 and the chance to flood .1% which pipe should the homeowner buy?