## Comment: Re:We're so screwed. (Score 1) 237

You're technically correct but they are only selectively dependent. If you don't die, the fact that you didn't die that year does not change the likelihood that you will die in the next year. This fact is sufficient for P(X and Y) = P(X) * P(Y) to hold for us because we are looking specifically at the probability that you DON'T die from terrorism over your lifetime. We make the dependency when you DO die irrelevant. That's why I took the path I did to answer the question "What are the chances you'll die from terrorism if you would otherwise live 75 years?"

To illustrate this, lets simplify things and take a look at a classic example: picking colored marbles from a jar. We are going to take a step back from the individual perspective and see what the probability is that a specific marble will get picked out of a larger population.

You have a jar with 3 marbles in it. 1 marble is yellow, {Y} (representing you) and 2 marbles are orange, {O1} and {O2} (representing other people). Every year, 1 marble is removed from the jar by a terrorist (representing death). And at the end of every year, 1 orange marble is added to the jar (representing someone else being born).

In year 1, there are 3 possible outcomes. 1 where the yellow marble is chosen. 2 where an orange marble is chosen.

Outcome 1: {Y}

Outcome 2: {O1}

Outcome 3: {O2}

At the end of year 1, orange marble {O3} is added. In year 2, there are 9 possible outcomes. We can apply the formula from my previous post to this. What does it say?

P(yellow will be picked over 2 years) = 1 - ((1 - (1/3))^2) = 1 - ((2/3)^2) = 1 - 4/9 = 5/9

So we would expect 5 of the outcomes to have yellow picked. Here's a table of the outcomes:

___Yr1__Yr2__

O 1 {Y}__ {O1}

U 2 {Y} __{O2}

T 3 {Y} __{O3}

C 4 {O1}_{Y}

O 5 {O1}_{O2}

M 6 {O1}_{O3}

E 7 {O2}_{Y}

# 8 {O2}_{O1}

_ 9 {O2}_{O3}

As represented by the math, there are 5 out of 9 outcomes in this table where yellow was picked. You can take this to 3 years and beyond. At 3 years, we would expect to see 8 in 27 outcomes where yellow was not picked. This makes sense if you look at the table above because outcomes 5, 6, 8, and 9 are the only ones that can generate a new outcome where yellow was not picked. In the new table, they generate 2 such outcomes each and 2 * 4 = 8.

Hopefully that clears things up a bit.