Fun with Bayes!

[kent_allard_jr]

I'm always happy when xkcd does stat jokes:



I may talk about Bayes' Theorem in class this semester (the first time I'll be doing so). For those who enjoy these little games... Assume only 1 in 2 million Americans knows 'that statistic.' If you walk down the road and find an American killed by lightening, what's the chance that he knew it?

Comments

[avram]

Taking the US population as 300 million (to make the math easy), that'd mean that 150 Americans know that statistic, and if one in six of them dies (I'm assuming that Munroe means rate of death by lightning strike even though he just says death rate) of lightning strike in a year, that's 25/year who know the statistic and die.

Taking the cartoon's stated figure of 45 Americans killed by lightning each year, which should include the 25 described above, that means that 55% of lightning deaths are people who know the statistic.

[kent-allard-jr.livejournal.com]

My result was close: I said P(A) was the chance of dying by lighting strike (1/7,000,000), P(A|B) was the chance of dying if you knew the stat (1/6) and P(B) was the chance of knowing the stat (1/2,000,000). Plug 'em into Bayes and you get (1/6)*(1/2,000,000)/(1/7,000,000)=7/12 or 58%. Since I never studied Bayesian Statistics, though, I may be doing something wrong here.

[kokoinai.livejournal.com]

The discrepancy is from agrumer's population assumption. 45 * 7mil is 315mil: using agrumer's method with 315mil yields exactly 58.33333333333... which is 7/12ths. Math works!

[avram]

But 315 million is high; most sources I'm seeing report somewhere in the 307-310 million range.

I figure our estimates are close enough, given the imprecision of the data sources.

[feiran.livejournal.com]

Bayes FTW. I miss stats class. :)

[bigscary.livejournal.com]

Go into epidemiology, use stat always and forever.