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

question 38

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?

---

Definitions:

Saturation

In a chemical context, the point at which a solution can no longer dissolve more of a solute; in color theory, the intensity of a color.

Subtractive Color

A color model in which colors are created by subtracting light from a white background using color filters, typical in printing.

Perceptual Experiences

The subjective interpretation of sensory information, which constitutes the individual's experience of the world.

Raw Sensations

Relates to the basic, immediate experiences that arise from stimuli affecting sensory receptors, before undergoing significant mental processing.