slides - John L. Pollock
... number of simple propositions, there is a completely intractable
number of logically independent probabilities.
» Given just 300 simple propositions, there will be 2300 logically
» 2300 is approximately equal to 1090.
» Recent estimates of the number of elementary particle ...
Notes on Bayesian Confirmation Theory
... psychologically real.
The formal apparatus comes very easily. Credences are asserted to be,
as the term subjective probability suggests, a kind of probability. That is,
they are real numbers between zero and one, with a credence of one for a
theory meaning that the scientist is practically certain t ...
conditional probability - ANU School of Philosophy
... is 1/6; this is an unconditional probability. But the probability that it lands with
‘5’ showing up, given that it lands with an odd number showing up, is 1/3; this
is a conditional probability. In general, conditional probability is probability given
some body of evidence or information, probabilit ...
Slides - Rutgers Statistics
... • There are two ways in which an agent’s space could
fail to be regular:
– 1) Her probability function assigns zero to some member of
F (other than the empty set). Then her second and third
grades come apart for this proposition.
– 2) Her probability function fails to assign anything to some
... 17. A parking lot has seventy parking spaces numbered from 1 to 70. There are no cars in the parking lot when
Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she
parks is greater than or equal to 30?
Probability and Forensic Science
... Given the use to which our assessment is being
Given the use to which our assessment is being
put, it is desirable that our assessment is not
wholly based on intuition
wholly based on intuition
Is there a way in which we can do this?
Declarations of Independence
... have zero probability, the converse is not true—even in finite spaces. For instance, rational
agents (who may have credences over finite spaces) may—and arguably must4—have irregular
probability functions, and thus assign probability 0 to non-trivial propositions.
Probability theory and statistics a ...
... Some contemporary writers appear to believe that the inductive
probability of a proposition is some person’s degree of belief in the
proposition. Degree of belief is also called subjective probability, so on
this view, inductive probability is the same as subjective probability.
However, this is not ...
Probabilistic thinking and probability literacy in the context of risk
... much less convincing. In such a single case, with chance, everything is possible.
However, once people have decided about their approach and strategy, and the outcome
is known to them, they start to re-interpret the course of action. Depending on their
character, some claim that whatever they do, t ...
Empirical Interpretations of Probability
... choose, there exists a process of measurement such that the result of applying
that process of measurement to the table will yield a result that will (probably)
differ from four by less than 6. It does not seem that the verification or
falsification of assertions of probability are any more problema ...
How bad is a 10% chance of losing a toe?
... 15% of all the responses to the prevention question were
at the maximum of 5.
The raw badness judgments do not correspond directly
to EU. If they did, the judgments for probabilities of .001,
.01, .1, and 1 would differ by a factor of 10. Although the
mean ratio of .01 to .001 is 7.3, the other rati ...
Odds are a numerical expression, always consisting of a pair of numbers, used in both gambling and statistics. In statistics, odds for reflect the likelihood that a particular event will take place. Odds against reflect the likelihood that a particular event will not take place. The usages of the term among statisticians and probabilists on the one hand, versus in the gambling world on the other hand, are not consistent with each other (with the exception of horse racing). Conventionally, gambling odds are expressed in the form ""X to Y"", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of how likely some possible future event is.In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet. Thus, odds of 6 to 1 mean the first party (normally a bookmaker) is staking six times the amount that the second party is. Thus, gambling odds of '6 to 1' mean that there are six possible outcomes in which the event will not take place to every one where it will. In other words, the probability that X will not happen is six times the probability that it will.In statistics, the odds for an event E are defined as a simple function of the probability of that possible event E. One drawback of expressing the uncertainty of this possible event as odds for is that to regain the probability requires a calculation. The natural way to interpret odds for (without calculating anything) is as the ratio of events to non-events in the long run. A simple example is that the (statistical) odds for rolling six with a fair die (one of a pair of dice) are 1 to 5. This is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 six event for every 5 times the die does not show six. For example, if we roll the fair die 600 times, we would very much expect something in the neighborhood of 100 sixes, and 500 of the other five possible outcomes. That is a ratio of 100 to 500, or simply 1 to 5. To express the (statistical) odds against, the order of the pair is reversed. Hence the odds against rolling a six with a fair die are 5 to 1. The probability of rolling a six with a fair die is the single number 1/6 or approximately 16.7%.The gambling and statistical uses of odds are closely interlinked. If a bet is a fair one, as in a wager between friends, then the odds offered to the gamblers will perfectly reflect relative probabilities. A fair bet that a fair die will roll a six will pay the gambler $5 for a $1 wager (and return the bettor his or her wager) in the case of a six and nothing in any other case. The terms of the bet are fair, because on average, five rolls result in something other than a six, at a cost of $5, for every roll that results in a six and a net payout of $5. The profit and the expense exactly offset one another and so there is no disadvantage to gambling over the long run. If the odds being offered to the gamblers do not correspond to probability in this way then one of the parties to the bet has an advantage over the other. Casinos, for example, offer odds that place themselves at an advantage, which is how they guarantee themselves a profit and survive as businesses. The fairness of a particular gamble is more clear in a game involving relatively pure chance, such as the ping-pong ball method used in state lotteries in the United States. It is much harder to judge the fairness of the odds offered in a wager on a sporting event such as a football match.