Is lowered probability of spending equals savings? This a really basic one and logic says: Yes given enough iterations.
But I am looking for validation

Situation: There is a 7% probability of expenses of 1000 occurring. I have a tool that then applied to the process has a 95% probability to reduce the chance of expenses occurring by 58-78% (mean at 60%). 
How do I calculate savings?
Not going into Risk-Adverse case as this is sensitive to how we define the Government's utility function

$\mathbb{E}[xpnse] = 0.05*(0.07*1000)+0.95*(0.6*(0.07*1000))$

Follows from Law of Large Numbers