The world can feel like a scary place.

Today, Australia's National Terrorism Threat Level is "Probable". Shark attacks are on the rise; the number of people attacked by sharks in 2000-2009 has almost doubled since 1990-1999. Travellers are at a high risk of getting the Zika virus in places where the disease is present, such as Brazil and Mexico.

However, despite their tragic outcomes, these events are all extremely rare.

Since 1996, only eight people have been killed by terrorism attacks in Australia. There have been 186 shark attacks in the 20 years from 1990 to 2009. Best estimates indicate that only 1.8 people for each million tourists would have contracted Zika at the Rio Olympics.

To be fair, it is extremely difficult to judge the incidence of rare events. Decision scientists study rare events by bringing people into the lab and asking them to make choices. For example, in their Nobel Prize-winning work, researchers Daniel Kahneman and Amos Tversky had people make choices between two options: one safe, one risky.