Political Probabilities

[Greg Ross]

Jack,

Assuming your second question was not entirely rhetorical...

Normally, if both boys were guessing, one would expect them both to score 25%. So if George scored 50%, I would wonder if he really was guessing. But setting aside disbelief,...

If George scored 0%, John would be expected to get 33%, since George would have eliminated one of the three wrong answers on each question. (But now I'm wondering how John would know which answers George gave. Methinks he peeked!)

Now, for each percent George gets right, that's 1% of the 33% that John could not get right. John's score, then can be calculated as 33% of 100% minus George's score. So if you want the score (S) where both will score the same, solve:

  S = 0.33*(1-S)
3*S = 1-S        ' Multiplying both sides by 3
4*S = 1          ' Adding S to both sides
  S = 0.25       ' Dividing both sides by 4

So, coincidentally, (and as might be expected by using intuition alone), if both boys "guess", they get the same score of 25%.

I assume your third question WAS intended to be rhetorical, but I'm going to respond with a couple of points anyway:

1. For each question on the real-world Iraq test, there are going to be more than 2 or 4 possible answers.
2. Among those possible answers, there will often be no correct answer. (Or even a good answer.)
3. HOPEFULLY, if John Kerry is elected, he won't simply RANDOMLY choose answers, but rather will use a measure of wisdom to select one of the better answers for each question, so his outcome in Iraq should be better than is hinted at by your scenario.

BTW: I actually tend to agree with your apparent opinion on the two current candidates, I just had to point out some logical flaws in your "argument".