A recent “*Ask the Experts*” question requested a risk assessment for skydiving versus grocery shopping.

The question was, *“(Do) you have a better (higher) chance of being killed going to the grocery store than you do going skydiving?”*

Thanks for a terrific question! Let’s approach it using simple math based on statistics and probability.

## Introducing Risk Assessments

A formal, quantified risk assessment would assess each risk by multiplying the expected cost by the probability of that risk actually occurring and by the number of times it might occur.

For example, if a card game costs you $1.00 when you draw an ace of hearts from a standard deck, then the assessed risk per draw is “$1.00 * (1/52) = $1.00/52”, or just under two cents. If you replace the drawn card each time, then shuffle and re-draw 104 times, then the assessed risk is $2.00 over all the draws. If drawing a king of diamonds only costs five cents, you can assess that risk and “draw” your own conclusions about playing this imaginary game.

In this article, the two situations are skydiving versus going grocery shopping. However, the only risk in question is death in either situation. Therefore the risk assessment concentrates on the probability of dying during either a parachute jump or a trip to a grocery store.

## Probability Theory versus Statistics in Risk Assessment

The earlier playing cards example used calculations from probability theory. We can count the number of cards in a deck, and assume random shuffles and fair deals. If you were playing against a card shark or stage magician, however, you might suspect the deck to be stacked against you. Then you would want to gather statistics in the real world, to learn what the odds truly are.

This Decoded Science expert has no theoretic basis for the risk of dying while skydiving or while grocery shopping. Therefore we need statistics from reliable sources.

## Statistics for Fatal Skydives in the USA

The United States Parachute Association (USPA) publishes statistics for skydiving fatalities in the USA. Their Skydiving Safety page reports 19 and 25 fatalities in 2012 and 2011, respectively. With an estimated 3,100,000 parachute jumps in each of those years, the annual risk assessment is a simple calculation.

- 19 / 3,100,000 = 0.0000006 deaths per jump in 2012.
- 25 / 3,100,000 = 0.0000008 in 2011.

This article will use “fatalities per 100,000 jumps” for ease of comparison. Over the 2011-2012 period, the average number of fatalities per 100,000 jumps in the USA is * 0.71*.

Since we used American statistics for skydiving, we must select all the rest of the data for the USA as well.

## Select Statistical Data

The US Census Bureau counted almost 308,750,000 persons in 2010.

The Centre for Disease Control’s “Deaths: Final Data for 2010” (PDF) reports the USA’s overall number of deaths in 2010 as 2,468,435.

Accidental death was the fifth leading cause, at 120,859.

Homicide ranked 16th, at a rate of 5.3 deaths per 100,000. Then “5.3 * 308,750,000 / 100,000 = 16,364” people were killed by other people. This would include shooting, stabbing, poisoning and other means.

The other deaths in the top 16 were mainly medical, so let’s use 137,223 deaths from accidents and homicides in 2010.

However, we can eliminate some of these deaths from the “grocery store trip” category.

Let’s exclude 3,782 drownings; 1,600 deaths on journeys on water or in the air; and 33,000 poisonings.

- 137,223 – 3,782 – 1,600 – 33,000 = 98,841 eligible deaths in 2010.

For the moment, let’s assume that all these deaths took place during trips outside the home, excluding airflights or cruises. So some of these people may have died during grocery shopping expeditions.

Decoding Science. One article at a time.