## Friday, July 03, 2015

### Perspective - 20 year family reunion probabilities

For at least two good reasons I’ve been doing a bit of planning. More on those reasons later, but first a digression to answer a relevant question.

What is the probability that, estrangement aside, our nuclear family will be able to do a reunion in 20 years? Let’s assume for simplicity’s sake, no major disruption of civilization and no major changes in US mortality rates by age. I’ll also exclude Kateva, who is healthy at age 10 but unlikely to break canine longevity records.

It’s not hard to do the rough calculations, unadjusted for gender, wealth, education or health, using a basic Life table. I'm looking for

tPx: probability someone aged x will survive for t more years.

and the formula based on a Life Table is:

Lx+t/Lx where Lx is the number surviving to age x

Lx can be found in the US 2010 Life Table. (Excel version can be downloaded from: ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Publications/NVSR/63_07/Table01.xlsx)

For my family the relevant values are:

Which gives survival probabilities for 20 years beyond current age as:

Where Product All is the product of each more-or-less independent probability. That is only about 50%, which is not so great. On the other hand, in the event of the cosmic calamity of my demise, I won't have much skin in the game. So the interesting number is the probability that Emily and kids make it assuming I do, which is Product “Impt” (important). That’s 71%.

Which is a useful number for my planning purposes and that future post I promised.

PS. I can remember when 20 years felt like a long time. It’s not.