Low Probability Events - Politicians with children in Iraq
What is the probability that 3 of the major candidates each have children serving in Iraq soon?
So if you don't hold anything against Obama whose children are too young to even consider joining the military as yet, what is statistically odd is the fact that of the other 3 presidential and vice presidential candidates (Biden, Palin and McCain) each will have a child serving not just in the military, which is rare in itself, but all will be in Iraq at the same time. That has to be a near impossibility. How impossible?
US military are currently serving in Iraq. 144,000
US Population between ages of 18 and 54: 158 million Americans
So the chance that a random American of military age is serving in Iraq is 144k/158 million or just a tad under 1 in 1,100. The probability that 3 folks picked at random are all in Iraq would be (1/1,100)^3 which works out to 1 in 1.3 billion.
You need to account for the fact that McCain has 6 adult children in total, Palin has 5, but only 1 is military age, and Biden has 3 adult children. So the probability that all three have at least one child in Iraq comes out to (1/1,100)*(6/1,100)*(3/1,100) which comes out to 1 in 74 million.. You could refine that calculation in many ways. It would make sense to use some age and gender specific probabilities because the universe of folks in the military is not exactly representative of the nation as a whole. No matter how you refine it, it gets to be a small small probability. If a random event, the chance that you win powerball this week is probably higher. What's it mean? Nothing is random about who makes up the small pool of folks who wind up running for President or Vice President to begin with. How that self-selection works?