Question

In a property liability case, a company can settle out of court for a loss of $350,000 or go to trial losing $700,000 if found guilty, or lose nothing if found not guilty. lawyers estimate the probability of a not-guilty verdict to be .8

How would I find the expected value of the amount the company can lose by taking the case to court?

Answer 1

Quite interesting. I have a purely mathematical solution, but I don't wan to use that in an everyday affair like this.
@Hero @Zarkon @phi

Answer 2

Answer is 140,000

Answer 3

@primeralph, don't hold yourself back.

Answer 4

@Hero But the bed; it's holding me back.

Answer 5

see https://en.wikipedia.org/wiki/Expected_value#Discrete_random_variable.2C_finite_case
The expected value of x = amount the company can lose by taking the case to court?
\[ E[x]= x_1 \cdot p_1 + x_2 \cdot p_2 \]
you have two outcomes: you lose the case (x= 700,000) or you win (x= 0)
They say " probability of a not-guilty verdict = .8 " (winning the case)
prob of losing the case is 1 - Pr(winning) = 0.2

so the expected loss is
\[ E[x]= 0 \cdot 0.8 + 700000 \cdot 0.2 = 140000 \]