On Coins, Dice, and Lethal Injections

“They told me there would be no math.” -- Chevy Chase as President Gerald Ford on Saturday Night Live, 1975.

What are the chances that if you could flip a coin 10 times it will not once turn up "tails?" In other words, what's the chance of 10 "heads" in a row? The odds can be calculated as:

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = (1/2)^10 = 0.001 = 0.1%

What are the chances you could roll a die ten times in a row and not have it once turn up "1?" In other words, what's the chance of getting somewhere between 2 and 6, ten times in a row? That answer can be calculated as:

5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6 = (5/6)^10 = .162 = 16%

Now here we go.  Texas has exonerated 2.4 people from death row for every 100 they have executed. (The other 49 states have exonerated 14 people from death row for every 100 they have executed.) Assuming that for each lethal injection in Texas there is a mere chance of 2 in 100 that the convict is innocent, what's the chance that Texas has not executed an innocent person among its 451 lethal injections?

(98/100)^451 = 0.011 = 0.01%

That's one chance in 10,000. And that assumes that the Texas death machine is 98% accurate.

Not bloody likely.

tsj

7 Apr 2010