Finished reading Chance

I haven't blogged in a while, so here we go.
I have updated the GANTT chart:


The last few chapters of Chance talk about a variety of things, such as The Birthday Problem, which I meantioned in an earlier blog (about the chances of two people having the same birthday). Amir Aczel also talk about a similar situation - the probability that 2 balls land in the same box, if a number of balls are dropped into a number of boxes at random. There are 2 equations that are stated which I found quite interesting:

"1.2 times the square root of the number of categories gives the number of 'balls' required for even odds that at least two share some characteristic.
And:
1.6 times the square root of the number of categories gives the number of 'balls' required for ninety-five percent probability that at least two share some characteristic."

So, if we go back to the Birthday Problem that I came across at the maths taster day, I can now work estimate:
1) 1.2 times the square root of 365 = 22.926, so 23 people have a 50 percent probability of at least one shared birthday.

2) 1.6 times the square root of 365 = 30.57, so 31 people have a 95 percent probabily of at least one shared birthday.

Now it is easy to see why, in my group of 50 people, there was an extremely high probability (97 percent) that we would find a shared birthday.

The book then goes on to talk about the normal curve:
"De Moivre discovered the "normal law of errors." He found out that when many random factors accumulate, they form a bell-shaped curves, with lesscommon valuse tailing off on either end, and the more average valuse grouping in the middle."
A few probabilities are stated, involving standard deviation, for example, "1. The probabilist that a normally distributed random quantitt will fall within one standard deviation of the mean is about sixty-eight percent."

Here is a picture of the normal distribution curve that I found on google.

And here is the website that the picture if from: http://www.igs.net/~cmorris/index_subject.htm

I already know these probabilities at they are used in the Statistics 1 module of the maths A-level.

The final chapter concludes the book:
"Probability is humanity's attempt to use pure mathematics to understand the un-understandable. It is our way of trying to learn something about the workings of chance. Chance remains forever untamable, for fate does what it wants to us and to the world around us."

This passage shows that Amir Aczel believes that pure randomness does exist, and probability is a way of helping us understand it. Nothing in the book proves or suggests that randomness does not exist, however Amir Aczel indicates that with enough maths, it is relatively easy to be able to predict random events, which therefore make them less random, and more of a pattern.