## Saturday, June 20, 2009

### Puzzle - The Tenth Roll

An ordinary dice (such as used in gambling) has six sides, so the probability that any one side will come out is one out of six, or 1/6.

Suppose your role a certain dice nine times. Each time the 1-dot turns up. What is the probablility that the 1-dot will turn up again onthe next roll? Is it better than 1/6, less than 1/6 or is it still 1/6?

singaporeshortstories.blogspot.com said...

Hi Mr Tan,

Ya, I got it correct.

This is what we have learnt in JC:

Let A be the event that the next roll gives 1 dot.

Let B be the event that the previous 9 rolls give 1 dot in each of the roll.

Let P= Probability

Let A|B= Event A occurs given event B occurs

P(A|B)= [P(A). P(B)] /P(B)
= P(A) = 1/6

A and B are both mutually exclusive events.

Aurvandil said...

If we apply this puzzle to the fund management industry, we can get some interesting outcomes.

In the fund management industry, there are lots of "superstar" fund managers These are people who are supposedly "gifted" and who are able to earn supernormal trading profits from the markets.

To get them to manage your money, clients like Temasek and GIC will literally pay millions of dollars.

So how do we determine fund managers are "gifted"? Well we use their past track record. If they had beaten the market in the past 9 years, then we assume that they will have a higher probability of beating the market again this year.

Now replace fund manager with dice and you can see how silly it is to believe these "gifted" fund managers. This is because even if that person was only average, blind chance would ensure that there would be a small group that beat the markets for 9 years.

The biggest irony is that if it is not blind chance, then there is a high chance you have found a ponzi scheme. Before the Madoff scheme was made public, there were numerous complants to the SEC that he was running a ponzi scheme. This is because the supernormal returns of his funds were statistically impossible.