Here is a small brain-teaser.
Let us take the example of a examination/ test centers, that run an exam throughout the year, every day of the year. Analysis of the past one-year data shows that 30% of the candidates pass the exam and 70% fail the exam, all over India.
The Bangalore test center handles around 1000 candidates per month, whereas the Mysore center handles around 100 per month. Over the last one year, both centers have shown the same 30 pass: 70 fail ratio.
For the month of June 2010, one center has reported 38% pass and another has reported 29% pass. Which center (Bangalore or Mysore) is more likely (has a higher probability) to have reported 38%? Why do you think so?
See my post dated August 3, 2010 for the answer and implications.