Probability Question

Miscellaneous and Personal Stuff I Must Share
1

So I was working last night when a customer told me that the New England Patriots were up 7 to nothing in the Super. Bowl. I heard nothing else until I was driving home. I turned on my car radio just in time to hear a touchdown had been scored to tie the game at 14 to 14. The game went into commercials before I heard who had scored that last touchdown. Disregarding what we know actually happened, what were the odds that Seattle was the last to score and tie the game?

2

My initial thought is that it’s a 2/3rd probability that Seattle scored the tying touchdown/PAT.

However, I’ll wait for the real statisticians to drop by and either confirm or ridicule me…

3

2 in 3 sounds right to me. There were three possible scenarios, and Seattle would score last in two of them. I suppose for completeness, you’d have to consider other ways each team could have scored the seven points you missed, but I suspect the odds would come out the same.

4

Still, the team that scored the touchdown to tie would have either previously had 7 points (highly probable), 6 points (possible) or 8 points (very improbable). In the unlikely events, Seattle must be the team that scored. But it is most likely the touchdown was scored by a team that had 7 points, a total the Patriots were known to have already had.

So it seems to me the likelihood is a little less than 2/3.

5

Doesn’t that make the implicit assumption that each of those possibilities are equally likely?

6

There are only two ways a team with 7 points can get to 14. Either a touchdown and extra point or two safeties and a field goal. The latter is extraordinarily unlikely.

However, the team with zero points could have had two field goals and a touchdown with a two point conversion. There are also several scenarios involving a single safety that total 14. Therefore I posit that the probability of Seattle scoring the touchdown in question is ever so slightly less than 2 out of 3.

7

If you knew New England had a 7-0 lead, there are only three ways the game could be tied 14-14 at the half:

  1. New England was up 14-0, and Seattle scored two straight touchdows,
  2. New ENgland was up 14-7, and Seattle scored a touchdown
  3. Seattle was up 14-7 and New England scored a TD.

Looks like a 2/3 chance Seattle scored last.