*Warning: if you think you may be disturbed by this topic, please stop reading now!*

*This is a rare non-IT blog post ... just something that came up in an email conversation and piqued my curiosity.*

__Introduction__
The statement -

**“You are 200 times more likely to die in a car crash than a plane crash!”**

- raises the following questions:

1) Where has this figure of 200 come from (how is this
quantified)?

2) How is this qualified?

The statement by itself, without further quantification
and qualification, is pretty meaningless.

__Well Defined Statitistics__
At this website - http://www.pbs.org/wgbh/nova/space/how-risky-is-flying.html
- there is a table with data provided by the U.S. Department of Transportation.
And it has the following interesting and well defined statistics:

**Motor Vehicles:**

1.3 deaths per 100 million vehicle miles

**Air Carriers:**

1.9 deaths per 100 million aircraft miles

*Note: The data is from 1999-2003.*

When you look at these statistics, Air Travel doesn’t
look that much safer than Motor Vehicular travel!

__Likeliness of Being Involved in a Fatal Car/Plane Crash__
Going back to the statement in question, can we use the
statistics above to reach this figure of 200?

Let us start with a thought experiment:

Consider a car with one person in.

Consider a plane with 200 people in.

Consider a trip of 1000 miles.

For the car, the number of these 1000 mile journeys
before its statistically likely there’ll be one fatal accident is:

(100’000’000/1.3)/1000 ~= 76’923

*Note: That is nearly 77 million miles or over 3000 times around the world!*

For the plane, taking into account that there are 200
people on board, the number of these 1000 mile journeys before its
statistically likely there’ll be one fatal accident (in which everyone on-board
dies) is:

(100’000’000/1.9)*200/1000 ~= 10’526’316

*Note: That’s over 10 billion miles or over 400’000 times around the world!*

And 10’526’316/76’923 ~= 136

So, in this case:

**“You are 136 times more likely to die in a car crash (if you’re the only one in the car) than a plane crash (if you’re one of 200 people on board) on a journey of the same distance!”**

__The Formula__
Notice that really the 1’000 miles above makes no
difference to the calculation, so we can create a formula for:

**“You are X times more likely to die in a car crash (if you’re one of Y people in the car) than a plane crash (if there’s Z people on board the plane) on a journey of the same distance!”**

(100’000’000/1.9)*Z/(100’000’000/1.3)*Y = X

Or:

X = 13Z/19Y

__So, Where Does the 200 Come From?__
In this case X = 200 and we can calculate a value of Z
that will solve the equation for different values of Y (people in the car)
using the formula:

Z = X*19Y/13

Z = 200*19Y/13

For Y = 1: Z ~= 292

For Y = 2: Z ~= 585

In other words:

**“You are 200 times more likely to die in a car crash (if you’re the only person in the car) than a plane crash (if there’s 292 people on board the plane) on a journey of the same distance!”**

**“You are 200 times more likely to die in a car crash (if you’re one of 2 people in the car) than a plane crash (if there’s 585 people on board the plane) on a journey of the same distance!”**

__Is There Any Truth in all This?__
No, it’s just “lies, damn lies, and statistics!”

*... Continuation ...*

__What about if we have 3 cars, each carrying 4 people?__
Again, let us use a thought experiment:

Consider we have a car with 4 people in.

Consider a trip of 1000 miles.

The number of these 1000 mile journeys before it's
statistically likely there’ll be one fatal accident is:

(100’000’000/1.3)*4/1000 ~= 307’692

The chance of having a fatal crash on that 1000 mile
journey (in which everyone on-board dies) is therefore:

1/307’692

If we have 3 cars, the chance all 3 are involved in a
fatal crash on the same journey, is 1/8 of the above.

Why 1/8?

There are only two possibilities per car - say 0 or 1; 3
cars which gives 8 possibilities (2*2*2 = 8); and the possibility of getting
three 1’s is 1/8 - which is illustrated below:

000

001

010

011

100

101

110

**111**

So, the chance of 3 cars of 4 people being involved in a
fatal crash on the same 1000 mile journey is:

1/307’692 * 1/8 = 1/2’461’536

__How does the Plane Fare?__
Consider we have a plane with 200 people in.

Consider a trip of 1000 miles.

The number of these 1000 mile journeys before its
statistically likely there’ll be one fatal accident is:

(100’000’000/1.9)*200/1000 ~= 10’526’315

The chance of having a fatal crash on that 1000 mile
journey (in which everyone on-board dies) is therefore:

1/10’526’315

How much safer is the journey in the plane?

10’526’315/2’461’536 ~= 4

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