Friday 23 July 2010

Reading through Chance...

The book begins with probability. "Probability is humanity's attempt to understand the uncertainty of the universe,to define the undefinable. A probability is a quantitative measure of the likelihood of a given event." Amir D. Aczel goes on to talk about probability in a similar way to the Statistics 1 module of the Maths A level.

He then moves on to talk about objective and subjective probability and the de Finetti Game. "Bruno de finetti(1906-1985) was an Italian statistician [...] Incredibly, he found a way to objectively measure subjective probability"

The de Finetti game assess someone's true subjective probabiliy. Amir D. Aczel uses the example of a friend saying that they are 100 percent sure that they will get a perfect score in a test that they have just done.
"Tell your friend the following. 'Let's play a game. You have a choice. You can either draw a ball from a bag that has ninety-eight red balls and two black balls. If you happen to draw a red ball, I will give you one million dollars. Or you can decide to wait to see how you did on the test, and if you receive a perfect score on that test I will give you one million dollars. What's your choice: draw or wait?' Presumably your friend will say, 'Draw from the bag.' If he doesn't, it means he really has a subjective probability of one hundred percent of acing the test. If your friend's decisionis 'draw,' you ask the next question: 'Now there are eighty red balls in the bag and twenty black ones. Do you want to draw,and if you obtain a red ball get a million dollars,or wait to see how you did on the test and get a million if you aced it?'" The game carries on like this until the person cannot choose between drawing or waiting. This is their actual subjective probability.

I think that this game would be a good thing to use in my presentation, as it will allow me to interact with the audience and make the presentation more intersting for them. I could begin by talking about how something may never be totally random because of probability, as probability can help us predict random events. This would lead me onto picking balls out of a bag. I could get the audience to pick a ball out of a bag of different coloured balls, and ask them if this is random, or perhaps it is a pattern that is too complicated for us to understand. I could then do the de Finetti game, to talk about why it is important to have objective probability when handling an event.

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