$1.(10$ pts$)$ A Monte Carlo simulation of a new gold mine calculated the following net

present values and their probability of occurrence.

NPV Probability

$ $5$ million $15\%$

$$7\mathrm{.}5$ million $25\%$

$$15$ million $35\%$

$$12\mathrm{.}5$ million $20\%$

$$20$ million $5\%$

What is the expected net present value of the gold mine?

Can you also go into detail of each step? I am uncertain why we do certain things