Probability and risk

Everyday radiation

Most important source is Radon gas.

Risks of daily life

In-class writing...

  1. It seems that it is safer to travel by car than by bicycle. If that's the case... why are so many more people killed in car accidents than in bicycle accidents each year?


  2. The chance of death by car accident is 1 in a million for each 50 km driven. The average car in the U.S. is driven ~ 12,500 miles in a year. What are the chances of death from a car accident over the course of a year for a person who drives this much over the course of a year? (1 mile = 1.6 km)

    Motor vehicle deaths by year, U.S.A.

We figured that you have about 1 chance in a million of dying from a heart attack in the next 2 days!

Probability: "frequentist view"

Start by figuring out how many people suffer a heart attack, and eventually how many die from a heart attack each year in the USA.

Now figure out what an average person's chance of dying from a heart attack is in one year...

For what time interval is your chance of dying from a heart attack 1 in a million?

Cost-benefit analysis

  • The market price for a single heifer is \$2500, so if a cow is stolen, I stand to lose $2500.
  • Would it be worthwhile to invest in a security system? how much?
  • How does probability come in?

The idea of expected cost....

What is the economic Value of 1 human life?

Bayesian view of probability

In the "frequentist" view of probability, you use history to *retrospectively* figure out the chances that some kind of event will happen.

But what about things that have never happened before?

The Bayesian interpretation of probability the probability of an event is the degree of belief (can be subjective) that it will happen.

In a Bayesian view...

  • Averaging the degree of belief of many people often leads to a better estimate than any one individual's views.
  • There is a precise formula (due to Thomas Bayes) telling you how to update your belief in the light of new facts.