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 $10 and that the homeowner must buy one of the two.

(a) (20 points) In terms of p, what are the probabilities for each node (A1, A2, B1, and B2)?

(b) (35 points) If the chance of a leak causing household damage is 2%, at what dollar amount of household damage is the owner neutral on which pipe to buy?