A contractor is building an office complex and needs to plan for water and electricity demand (sizes of pipes, conduits, and wires). After consulting with prospective tenants and examining historical data, the contractor decides that the demand for electricity will range between 1million and 150 million kilowatt-hours per day and water demand will be between 4 and 200 (in thousands of gallons per day). All combinations of electrical and water demand are considered possible. Let stand for water demand in thousands of gallons per day and the electric demand in millions of kilowatt-hours per day. Suppose that the contractor is interested in low demand. Let be the event where water demand is at least 100, and let be the event that electric demand is at least 115, and suppose that these values are considered low demand.

The contractor wishes to compute the probability that the total utility demand is low, meaning that the sum of water and electrical demand is at most 215. Let be the event that the sum of water and electrical demand is at most 215.