popper-logic-scientific-discovery

406
new appendices
of the brevity of that passage, I may perhaps explain this point here
again.
Consider the next throw with a homogeneous die. Let x be the
statement ‘six will turn up’; let y be its negation, that is to say, let y = x¯;
and let z be the information ‘an even number will turn up’.
We have the following absolute probabilities:
p(x) = 1/6; p(y) = 5/6; p(z) = 1/2.
Moreover, we have the following relative probabilities:
p(x, z) = 1/3; p(y, z) = 2/3.
We see that x is supported by the information z, for z raises the
probability of x from 1/6 to 2/6 = 1/3. We also see that y is undermined
by z, for z lowers the probability of y by the same amount from
5/6 to 4/6 = 2/3. Nevertheless, we have p(x, z) p(x) & p(y, z)