# Is lowered probability of spending equals savings? [closed]

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?

• This needs to be better phrased. How much agent's save will be determined by their preferences for risk. A more risk-adverse agent will save to cover more than the expected loss, while the risk-neutral agent will save to cover his expected loss. – hipHopMetropolisHastings Jan 31 '17 at 16:16
• Fair point. In this instance it's government... I would classify as risk-neutral. Could you please give samples for both? – PovilasID Jan 31 '17 at 16:23

## 1 Answer

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