A video game company uses three pieces of machinery to produce games. The company operates 365 days per year and the games produced each day can be sold at a profit of $10,000.
The three machines have a probability of failing on any given day of 1%, 2%, and 3% respectively. Thus the probability that they are all operational and the company is producing games on any day is approximately 94.11%.
The company is considering leasing a backup for each machine; the leases will cost $100,000 per year. Think of the backup machines in the same way we considered RAID disk drives; each pair of machines has a lower probability of failure than an individual machine. How much more profit will the company expect to earn if they have the backup equipment and will the additional profit cover the cost of the lease?