Monday, February 22, 2010

Probability

There's an interesting discussion on probability at William Brigg's blog.

Briggs claims, and is supported by some of his readers, that given

• I have some six sided object in my pocket
• Exactly one face is inscribed with '6'

we can conclude

• P(a '6' shows uppermost after a roll) = 1/6.

I, and some other readers, contend that no such statement can be made. The discussion is interesting because some, like myself, see probability as a description of reality, whereas others see probability as a description of a state of knowledge.

I'll be fascinated to see how this one turns out.

1 comment:

SteveBrooklineMA said...

Me too! I hope the discussion continues.

I would define a "coin" mathematically as a non-negative real-valued function P on {H,T} such that P(H)+P(T)=1. Equivalently, I would define a coin as an element p of the interval [0,1], identifying p with P(H) and (1-p) with P(T).

Does it make sense to say "p is in [0,1], thus p=1/2"? This seems equivalent to saying "You have a coin I know nothing about, thus the probability of heads is 1/2."

It doesn't make sense to me.