David Bee sent this one to the AP Stats EDG and it caught my eye:
At the end of each Court term the NYTimes has a chart showing how
many agreements there were between each of the 9C2 = 36 possible
pairings of the nine Justices. (There was something someone in the
Forum posted earlier that reminded me of this but I don't recall
it.) [For example, the highest percentage of agreements was between
Justices Scalia and Thomas (92 percent) and the lowest was between
Justices Stevens and Thomas (60 percent). Thus, for the 36 pairings,
60% <= in agreement <= 92% --- math and stat teachers should have it
I guess I always thought questions that got to the Supreme Court would be pretty much 50/50 propositions, and was surprised to find out that Justice Stevens, the longest serving of the Justices, who had the lowest percentage of voting with the majority, was still in the majority 73% of the time; and Roberts and Kennedy agreed with the majority a whopping 92%/90% of the time.
So the stats question is: If all nine judges voted randomly on each decision, what percentage of the time would they be in the majority. (a computer simulation is un-acceptable, come let us reason together)..
Those who want the original NY Times article may find it here.