# probability when large difference

Let's say the following is data for airplane accident death to total.

Country Sky        Total death       Total individual traveler
A                     30                    10,000
B                     60                    15,000
C                     3000               10,000,000


Is it possible to calculate probability of air accident probability for any traveler in A, B, or C skies by simply dividing total deaths over total travelers ? If some countries have low flight and others have very high number of flights can this affect the estimates ?

• First, you're analysis would be better if you used a metric more like: "# of deaths per 100,000,000 miles flown" (or something like that)... As for calculating the probability of an air accident, it depends on how accurate you want to your estimate to be. As a first-order approximation, you probably could use your suggested method and your result would probably be more accurate than just guessing "0" (but that's not saying it's the best approach available--just that it's probably better than, well, nothing). – Steve S Jul 28 '14 at 0:10

## 1 Answer

The division Total death by Total individual traveler gives the probability of dying in conditions A, B or C. Note that this is the probability of dying given that the person is a traveler. The global probability of dying in an air crash would have to take into account the probability of traveling at all.

If the number of flights is very different, the estimates will have different variances. There will be more uncertainty for the countries with low amount of flight. If sampling is independent and identically distribution (IID), the variance of the estimate decreases as $O\left(\frac{1}{N}\right)$ where $N$ is the sample size.