## Wednesday, November 16, 2011

### Odds

The other day a friend was asking: "which carrot should I take, this one or that one?", showing us two carrots of different shapes.

The other person present and myself simultaneously answered: "This one!", pointing to the same carrot. So my friend picked that carrot, commenting: "Wow, you guys made exactly the same choice. Amazing!", to which I replied ironically: "Yes, amazing! What are the odds?"

Compared to most people, it's hard to get me excited about chance events. In particular a 1-in-2 chance event doesn't get me to even raise an eyebrow. Here's my scale:

1 in 10: raised an eyebrow
1 in 100: quite surprised
1 in 1000: skeptical, then amazed
1 in 10000: skeptical, then still skeptical (in spite of evidence).
1 in 100000: impossible. Not even worth refuting.

1. How about the odds that in a given day when you look at your watch the time is palindromic or better yet, the hours and the minute is the same... I have not tried checking the probability of such events occurring in a day...

2. So you're skeptical about 1 in 10000 ? Here is some evidence. Last Saturday I drove into a ski resort for a family vacation and left the car in a public car park, in spot number 4008.
At the hotel our ski locker had a combination lock. Combination number: 4008 again!
Still skeptical ?

3. There are not 10000 spots the number of the car spot was a random number from a finite set of size a few hundreds, not 10000.

As to combination locks, do you know how they are chosen? They're not random but chosen so that they're easy for the customer to memorize. (Maybe.)

4. Yes, there were not 10000 spots. I assumed that the combination locks were chosen at random, but don't really know. It seems reasonable to assume that they have no connection to the numbers chosen for the car spots.