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Definition
| An outcome is the result of an experiment or other situation involving uncertainty. |
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Term
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Definition
The set of all possible outcomes of a probability experiment is called a sample space.
The sample space is an exhaustive list of all the possible outcomes of an experiment. (sometimes S)
Experiment Rolling a die once:
Sample space S = {1,2,3,4,5,6}
Experiment Tossing a coin:
Sample space S = {Heads,Tails}
Experiment Measuring the height (cms) of a girl on her first day at school:
Sample space S = the set of all possible real numbers |
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Term
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Definition
An event is any collection of outcomes of an experiment.
Formally, any subset of the sample space is an event.
Any event which consists of a single outcome in the sample space is called an elementary or simple event. Events which consist of more than one outcome are called compound events. |
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| Symbols to know if A and B are two events in the sample space |
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Definition
AυB (A union B) = 'either A or B occurs or both occur' A∩B (A intersection B) = 'both A and B occur' (A is a subset of B) = 'if A occurs, so does B' A' or A = 'event A does not occur' Φ(the empty set) = an impossible event S (the sample space) = an event that is certain to occur |
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Definition
Rule One: it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out |
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| Formula for Rule One: Relative Frequency |
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Definition
number of times A occurred
number of times the trial was repeated |
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| Criteria for Rule One: Relative Frequency |
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Definition
An approximation is being obtained instead of an exact value; As the total number of observations ↑, the corresponding approximations get closer to actual probability; It can be used for events that do not have equally likely results. |
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| Rule Two: Classical Approach to Probability |
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Definition
| Approach in which the probability of an event is determined by dividing the number of ways the event can occur by the total number of possible outcomes. |
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| Equation for Rule Two: Classical Approach |
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Definition
number of ways A can occur total number of outcomes |
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| Criteria for Rule Two: Classical Approach |
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Definition
| When all outcomes are equally likely, like drawing a name out of a hat |
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Term
| Rule Three: Subjective Probability |
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Definition
| A subjective probability describes an individual's personal judgement about how likely a particular event is to occur. It is not based on any precise computation but is often a reasonable assessment by a knowledgeable person |
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| Criteria for Rule Three: Subjective Prob. |
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Definition
| Is not based on actual, frequent values, but rather expresses an educated guess. |
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Term
| What is the Complement of an event |
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Definition
| All outcomes in which the original outcome does not occur |
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| How to show your data of probabilities |
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Definition
Give exact fractions or decimals, or round decimals to three significant digits. |
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Definition
| Odds m:n, read as m to n, in favor of an event mean we expect the event will occur m times for every n times it does not occur. |
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Term
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Definition
| Odds m:n, read as m to n, against an event mean we expect the event will not occur m times for every n tiems it does occur |
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Definition
The ratio of net profit gained to the amount bet (net profit) : (amount bet) |
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Definition
| Any event combining two or more simple events. |
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Term
| What is the Addition Rule |
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Definition
| The addition rule is a result used to determine the probability that event A or event B occurs or both occur |
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| What is the Formal Addition Rule |
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Definition
where P(A and B) denotes the probability that A and B both occur at the same time as an outcome in a trial of a procedure. P(A or B) = P(A) + P(B)- P(A and B) |
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| Mutually Exclusive(disjoint) Events |
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Definition
| Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together. |
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Term
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Definition
The multiplication rule is a result used to determine the probability that two events, A and B, both occur. P(A∩B)=P(A)P(B) the probability of the joint events A and B is equal to the product of the individual probabilities for the two events |
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Definition
| A picture of the possible outcomes of a procedure. |
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Definition
| P(A | B) = the conditional probability that event A occurs given that event B has occurred already |
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Term
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Definition
| P(B | A) = the conditional probability that event B occurs given that event A has occurred already |
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Term
| What is an Independent Event |
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Definition
| Events that have no influence on eachother |
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Term
| What is a Dependent Event |
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Definition
| Events for which the occurrence of any one event affects the probabilities of the occurences of the other events. |
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Definition
P(at least one)= 1-P(none) You can find the prob. that NONE of the events will occur, then find the complement |
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| What is a Conditional Probability |
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Definition
| A Conditional Probability of an event is a prob. obtained with the additional information that some other event has already occurred. |
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| What is the Factorial Notation |
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Definition
N!=n, n-1, n-2, n-3... ex: 4!=4*3*2*1=24 |
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Term
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Definition
nPr = n!
(n- r)! the number of permutations of r items selected from n different available items |
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| What is the Combination Rule formula |
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Definition
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