Expected value word problem

[jmasta]

Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 91.3%. If BIC charges a premium of 5,200 silver coins and would pay a death benefit of 93,000 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC?
Round to the nearest silver coin as needed. If the expected value is a loss to BIC, enter your answer as a negative number.

How do I break this down into a solvable formula?

[Guest]

The expected value is a weighted average of the value of every outcome, where the weights are the probability a certain outcome occurs.

There are two outcomes the insured survives, or the insured dies.

The insured survives happens with probability [tex]= 0.913[/tex],
and the insurance company makes [tex]5200[/tex] silver coins (the premium)

The insured dies happens with probability [tex]= 0.087[/tex],
and the insurance company makes [tex]5200-93000 = -87800[/tex] silver coins (the premium minus the death payout)

So the expected value is [tex]0.913\times 5200+0.087\times-87800 = −2891[/tex] silver coins.

Hope this helped,

R. Baber.