An office machine costs $10,000 to replace unless a mysterious, hard-to-find problem can be found and fixed. Repair calls from any service technician cost $500 each, and you’re willing to spend up to...

An office machine costs $10,000 to replace unless a mysterious, hard-to-find problem can be found and fixed. Repair calls from any service technician cost $500 each, and you’re willing to spend up to $2,000 to get this machine fixed. You estimate that a repair technician has a 25% chance of fixing it.

(a) Create a probability model for the number of visits needed to fix the machine or exhaust your budget of $2,000. (That is, there can be at most four visits.)

(b) Find the expected number of service technicians you’ll call in.

(c) Find the expected amount spent on this machine. (You must spend $10,000 for a new one if you do not find a vendor that repairs yours.)