A pharmaceutical firm can develop a patentable face cream using either of two independent processes, each of which has a 25 percent chance of costing $5 million, a 25 percent chance of costing $10 million, and a 50 percent chance of costing $20 million. If the firm can determine the true cost of both processes after spending $2 million on each, what is the minimized expected cost of developing the patent?

Solution: 12.313

Any ideas HOW to arrive at 12.313?