It was our use of probability theory as logic that has enabled us to do so easily what was impossible for those who thought of probability as a physical phenomenon associated with "randomness". Quite the opposite; we have thought of probability distributions as carriers of information.
Probability and expectation are not the same. Its probability and probability times the pay off.
The source of Pyrrhonism comes from failing to distinguish between a demonstration, a proof and a probability. A demonstration supposes that the contradictory idea is impossible; a proof of fact is where all the reasons lead to belief, without there being any pretext for doubt; a probability is where the reasons for belief are stronger than those for doubting.
It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability.
According to theism, if a universe is to have any probability of existing, this probability is dependent upon God's beliefs, desires and creative acts. But the Hartle-Hawking probability is not dependent on any supernatural considerations; Hartle and Hawking do not sum over anything supernatural in their path integral derivation of the probability amplitude.
Anything is possible, but not always probable. Innovators increase the probability of the impossible.
With caution judge of probability. Things deemed unlikely, e'en impossible, experience oft hath proved to be true.
The grand assertion is that you must see the world through probability and that probability is the only guide you need.
Impossible is not a fact. It's an opinion. Impossible is not a declaration. It's a dare. Impossible is potential. Impossible is temporary. Impossible is nothing
The probability that we will get into a car accident is a million times higher than the probability we will suffer as a result of terrorist act.
The risk of an investment is described by both the probability and the potential amount of loss. The risk of an investment-the probability of an adverse outcome-is partly inherent in its very nature. A dollar spent on biotechnology research is a riskier investment than a dollar used to purchase utility equipment. The former has both a greater probability of loss and a greater percentage of the investment at stake.
It is almost possible to predict one or two days in advance, within a rather broad range of probability, what the weather is going to be; it is even thought that it will not be impossible to publish daily forecasts, which would be very useful to soci.
There exists a world. In terms of probability this borders on the impossible. It would have been far more likely if, by chance, there was nothing at all. Then, at least, no one would have began asking why there was nothing.
The price of freedom is the probability of crime. The price of protection is the probability of slavery.
I've debated many economists who claim to specialize in risk and probability: when one takes them slightly outside their narrow focus, but within the discipline of probability, they fall apart, with the disconsolate face of a gym rat in front of a gangster hit man.
If you get rid of emotion for a minute and think about the threat of terrorism statistically, it's not even there. The probability that you will slip on a wet floor in your bathroom and die is a thousand times higher than the probability of you dying as a result of terrorism.