Probability Flashcards
Define: numerical coefficient of probability.
A number that describes the likelihood, or probability, of the occurrence of an event. Its possible values range from 0 (impossibility) to 1 (certainty).
What are the two senses of probability?
- the apriori conception
2. the relative frequency conception
Define: a priori theory of probability.
A theory in which the probability ascribed to a single event is a fraction between 0 and 1, of which the denominator is the number of equipossible outcomes, and the numerator is the number of outcomes in which the event in question occurs. Thus on the a priori theory, the probability of drawing a spade at random from a deck of playing cards is 13/52.
Define: relative frequency theory of probability.
The view of probability in which the probability of a simple event is determined as a fraction whose denominator is the total number of members of a class, and whose numerator is the number of members of that class that are found to exhibit a particular attribute that is equivalent to the event in question.
For both senses of probability, probability is always relative to the ____.
evidence
Define: calculus of probability.
A branch of mathematics that can be used to compute the probabilities of complex events from the probabilities of their component events.
Define: product theorem.
In the calculus of probability, a theorem asserting that the probability of the joint occurrence of multiple independent events is equal to the product of their separate probabilities.
Define: independent events.
In probability theory, events so related that the occurrence or nonoccurrence of one has no effect upon the occurrence or nonoccurrence of the other.
What is this equation? P(a and b) = P(a) x P(b)
product theorem (for independent events)
Define: addition theorem.
In the calculus of probability, a theorem used to determine the probability of a complex event consisting of one or more alternative occurrences of simple events whose probabilities are known. The theorem applies only to mutually exclusive alternatives.
Define: mutually exclusive events.
Events of such a nature that, if one occurs, the other(s) cannot occur at the same time. Thus, in a coin flip, the outcomes “head” and “tails” are mutually exclusive events.
What is this equation? P(a or b) = P(a) + P(b)
addition theorem (for mutually exclusive events)
How do you calculate probability if you are dealing with alternate events that are not mutually exclusive?
Add the probabilities, but first, break down the set of favourable cases into mutually exclusive events. E.g. at least one head out of two coin tosses? Possible favourable outcomes: head-tail, tail-head, head-head. Outcome probabilities: 1/4 (each). Probability of getting of these outcomes? Add the probabilities. 1/4 + 1/4 + 1/4 = 3/4. Or, conversely, find the probability of the unfavourable outcome and subtract it from 1.
Define: expectation value.
In probability theory, the value of a wager or an investment; determined by multiplying each of the mutually exclusive possible returns from that wager by the probability of the return, and summing those products.
What is this equation? (return yielded * probability) + (return yielded * probability)
expectation value
