All the different kinds of probability 
are governed by the same basic rules. 
A priori probabilities are governed by 
those statistical probabilities follow 
these rules, subject to probabilities 
should follow these rules. 
But what are these basic rules? 
We're going to look at four basic rules. 
The first one governs simply negation. 
So you toss a coin and you get tails. 
What's the probability that you get 
tails? 
We said one in two or.5. 
Now, 
what's the probability that you do not 
get tails? 
Well, that means that's the probability 
that you get heads. 
So it's also 5.. 
It's one minus the 5. probability of 
tails gives you the.5 probability of not 
getting tails, that is, of getting heads. 
Well, that's really simple, because there 
are only two possibilities. 
What about a die? 
You roll a die and you get a two. 
What's the probability that you'd get a 
two? 
Well it's one in six. 
What's the probability that you would not 
get a two? 
Well, not getting a two is getting either 
one, or three, or four, or five, or six, 
so there are five possibilities of not 
getting a two, and that means that, that 
five times out of six you do not get a 
two. So the probability of not getting a 
two is one minus the probability of 
getting a two. 
The probability of getting a two is one 
in six, so the probability of not getting 
a two is five in six. 
So our rule is basically that the 
probability that an event will not occur 
is one minus the probability that the 
event will occur. 
And we can put that in symbols like this. 
You put PR for probability and then in 
parentheses you put what it's the 
probability of. 
We're going to use H for hypothesis or 
the event that we're testing the 
probability for. 
And the little squiggle or tilde means 
not, 
just like it did when we were talking 
about propositional calculus a few weeks 
ago. 
So, the probability of not the 
hypothesis, is equal to one minus the 
probability of the hypothesis. 
That's basically the rule for 
probabilities of negations. 
And we explained why it holds, because 
certainty is one. 
The thing happening and the thing not 
happening have to add up to one, because 
it's gotta either happen or not happen, 
so one minus the probability that it 
happens is gotta be the probability that 
it does not happen. 
So hope now the rule makes sense, and 
that you can apply it in a couple of 
exercises.