Unless Maine also repeals their use of instant runoff voting for the presidential election, their own votes won't count toward the national popular vote. The compact makes no provision for counting ranked ballots, and there isn't really any fair way to do so anyway.
I have a bolo tie whose slide ornament is carved anthracite.
I've never shoveled coal.
Bob said he's coming, but Janice said they can't make it.
Fish would eat you if they got the chance.
Can we just let gender-neutral toilets be the default so we can all stop worrying this? The fact that the stranger shitting next stall over may or may not have a penis is not a problem. Having to scrape turds off my shoe because someone followed this guy's advise and shat on the sidewalk makes it my problem.
Not sure about MIchigan in particular, but other states have, in relatively recent history, given ballot access to presidential candidates who were unambiguously constitutionally ineligible for the office. It doesn't make much sense to me either, but apparently neither the 14th amendment, nor any other federal law restricts who can run for president, merely who can hold the office if elected.
I see some correct solutions for the 50% case here already, so this reply is going for a perfect score within two tries.
There are 16 ways to answer the quiz, one of which is correct. Assuming you don't repeat your previous answers, two attempts give you a 2/16 or 1/8 chance that one of them is perfect.
Now if you get feedback between your attempts, you should be able to do better. Let's see by how much and break it into cases:
Your first guess is already perfect. This happens 1/16 of the time. No further guessing is needed.
Your first guess is 50% correct. This happens 3/8 of the time. Picking one of the unguessed answers improves your score to 100% 1/6 of the time.
Your first guess is completely wrong. This happens 9/16 of the time. Picking different answers for both questions wins 1/9 of the time.
So the overall chance of a perfect score is the weighted sum of these cases or 1/16 + (3/8 * 1/6) + (9/16 * 1/9) = 3/16.
Wordle rules: Yellow letters present in another position; Grey letters are unused.
Took me longer than usual to find anything that fit.
One consequence of this, even though it only applies to the primary and even if it is reversed on appeal, is to effective kill any momentum the NPVIC might have had.
It really punctuated the fact that there is no such thing as a national vote when voters from different states aren't even presented with the same choices. With the electoral college in place, this mostly doesn't matter, but NPVIC would encourage the most partisan states to run up the score for their guy by any means possible.
I usually promote approval for its simplicity and intuitiveness. STAR also seems respectably decent, and a significant improvement over plurality and IRV.
Since this is everyone's favorite example of telescoping sums, let's do it another way just for giggles.
Combinatorial proof
The denominator is P(n+1, 2) which is the number of ways for 2 specified horses to finish 1st and second in an n+1 horse race. So imagine you're racing against horses numbered {1, 2, 3, ....}. Either you win, which has probability 0 in the limit, or there is a lowest numbered horse, n, that finishes ahead of you. The probability that you beat horses {1,2, ... , n-1} but lose to n is (n-1)! / (n+1)! or P(n+1, 2) or 1/(n^2^+n), the nth term of the series. Summing these mutually exclusive cases exhausts all outcomes except the infinitesimal possibility that you win. Therefore the infinite sum is exactly 1.