
39Probability Theory
To further exemplify, suppose ΔI = $2 million, ΔM = $10 million. Moreover, assume the spill
is relatively unlikely p = 0.2. Calculating the cost using Equation 2.27 we get ΔC = ΔI − ΔM×
p = 2 − 20 × 0.2 = −2 and because it is negative we decide to invest in the protective measure.
We can investigate what would happen if the probability p were higher or lower by plotting
ΔC vs. p (Figure 2.10). We see that when 0 ≤ ΔM <$2 million, the cost difference ΔC is never
negative and we always choose A
2
. Then when ΔM = $2 million, the spill would have to occur
with certainty (p = 1) for the options to be equal. As we increase ΔM