Probability Flashcards

1
Q

Define: numerical coefficient of probability.

A

A number that describes the likelihood, or probability, of the occurrence of an event. Its possible values range from 0 (impossibility) to 1 (certainty).

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2
Q

What are the two senses of probability?

A
  1. the apriori conception

2. the relative frequency conception

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3
Q

Define: a priori theory of probability.

A

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.

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4
Q

Define: relative frequency theory of probability.

A

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.

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5
Q

For both senses of probability, probability is always relative to the ____.

A

evidence

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6
Q

Define: calculus of probability.

A

A branch of mathematics that can be used to compute the probabilities of complex events from the probabilities of their component events.

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7
Q

Define: product theorem.

A

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.

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8
Q

Define: independent events.

A

In probability theory, events so related that the occurrence or nonoccurrence of one has no effect upon the occurrence or nonoccurrence of the other.

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9
Q

What is this equation? P(a and b) = P(a) x P(b)

A

product theorem (for independent events)

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10
Q

Define: addition theorem.

A

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.

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11
Q

Define: mutually exclusive events.

A

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.

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12
Q

What is this equation? P(a or b) = P(a) + P(b)

A

addition theorem (for mutually exclusive events)

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13
Q

How do you calculate probability if you are dealing with alternate events that are not mutually exclusive?

A

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.

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14
Q

Define: expectation value.

A

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.

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15
Q

What is this equation? (return yielded * probability) + (return yielded * probability)

A

expectation value

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