ABSTRACT
Rather than give my suggested version of an F.R.P.S. straight away, I will consider some preliminary versions which might more naturally suggest themselves. By criticizing and improving these I will proceed to the rule which will finally be advocated. As indicated at the end of the last chapter I will begin with the rule of d’Alembert and Buffon (R.l) which stated roughly that we will regard a hypothesis H as falsified if the observed event has a low probability given H. Against this rule a simple but fatal objection can be raised. I have in fact already mentioned this point. Suppose we are tossing a coin and have the hypothesisthat the events are independent with prob (heads) = https://www.w3.org/1998/Math/MathML"> 1 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203828793/ecd34538-6a11-4738-a799-0c17881c8935/content/inline-math_63_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . Suppose we have a million tosses and observe exactly the same number of heads andtails. The probability of this event is of course https://www.w3.org/1998/Math/MathML"> 1 , 000 , 000 C 500 , 000 ( 1 2 ) 1 , 000 , 000 = 0.0008 ( to 1 sig . fig . ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203828793/ecd34538-6a11-4738-a799-0c17881c8935/content/math_46_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
