Wow, your understanding of statistics is even worse than I thought.
You saying this, doesn't make it so. At the risk of dumbing this down enough for you to grasp what is obvious to some of us:
A man is standing in an airport terminal. He's planning on flying from where he is to somewhere else. He's curious about the odds that he might die in a plane crash. At that moment, for him, his odds are exactly the same as the odds that the plane he's going to get on will crash resulting in his death
. Those odds are identical whether he's alone on the plane, or if there are 300 other people on the plane with him. His odds of dying are equal to the odds of the plane crashing in a manner that will result in his death. Period. End of story.
Thus, the odds of any specific traveler dying in a plane crash is equal to the odds of any given plane crashing (fatally) while traveling a number of miles equal to the flight he's taking. If one plane crashes for every 100,000 miles in which planes fly in the US, and he's traveling 1,000 miles by plane, then his odds of dying are 1 in 100.
Counting up the total number of people who've died in plane crashes over a period of time, and then calculating the total number of miles each passenger has flown
over that period of time and then dividing one by the other is useful for calculating broad travel statistics, but it does not actually tell the individual traveler his odds of dying on any given trip.
You seriously can't see why? That's just bizarre.
EDIT: Oh. And I think I got the relationship backwards. The calculation you're doing would make his odds of dying increase the more people there are on the plane, not decrease as I said earlier. Here's why:
Passenger miles is a calculation of the total number of passengers who've traveled X distance. Thus, if a plane travels 1000 miles with 1 passenger on it, that's 1000 passenger miles. If that same plane travels the same distance with 300 passengers on it, that's 300,000 passenger miles. If we calculate the rate of fatalities from air travel at say one death per 30 million passenger miles (how many passengers die over time compared to the total number of passenger miles over that same period), then this presents us with a quandary. The plane in the first instance is only going 1000 passenger miles, the plane with 300 people on it is traveling 300,000 passenger miles. Thus, the second case is 300 times more likely to result in fatality based on the statistics (since we're "traveling" 300 times as far relative to the value we're using to calculate our fatality rate). This would lead someone to conclude that he's 300 times more likely to die on that plane than the other.
This is obviously not correct. His odds of dying are the same in each case. What changes is that the "weight" of a plane crash with 300 passengers is greater, since 300 people would die if it crashes. Thus, from a "total air fatality" statistical perspective that plane is at greater risk. But from the point of view of a single passenger, he's not.
Get it yet? Edited, Mar 24th 2011 7:06pm by gbaji