Review of Basic Probability Rules
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| What do we mean by the term Probability? | Probability is a measure of the likelihood of a random phenomenon or chance behavior. Probability describes the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty.
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| Describe the Law of Large Numbers. | As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.
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| How is the term "experiment" used with respect to probability? | In probability, an experiment is any process that can be repeated in which the results are uncertain.
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| What is a Sample Space? | The sample space, S, of a probability experiment is the collection of all possible outcomes.
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| What is an Event? | An event is any collection of outcomes from a probability experiment. An event may consist of one outcome or more than one outcome.
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| In order to be a Probability Model, what is required? | A probability model lists the possible outcomes of a probability experiment and each outcome’s probability and must satisfy two rules: 1) 0 ≤ P(E) ≤ 1, for any event E , and 2) the sum of the probabilities of all the outcomes must equal 1.
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| What is the probability of an impossible event? | If an event is impossible, the probability of the event is 0.
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| What is the probability of a certain event? | If an event is a certainty, the probability of the event is 1.
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| Given S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and E ={2, 3, 5}, what is P(E)? | In general, P(E) = N(E)/N(S). Since there are 3 ways for “E” to occur and there is a total of 10 outcomes in “S”, P(E) = 3/10 = 0.3.
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| How is the probability of an event, E, approximated using the Empirical approach? | The probability of event E, using the Empirical method, is approximately the number of times event E is observed, divided by the number of repetitions of the experiment. That is, P(E) ≈ (Frequency of E)/(Number of repetitions of the experiment)
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| What does it mean for two events to be "disjoint"? | Two events are disjoint if they have no outcomes in common. Another name for disjoint events is mutually exclusive events.
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| What is the "Addition Rule for Disjoints events"? | If two events E and F are disjoint (or mutually exclusive), P(E or F) = P(E) + P(F).
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| What is the General Addition Rule for P(E or F)? | In general, P(E or F) = P(E) + P(F) – P(E and F).
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| How is the "Complement" of an event defined? | Let S denote the sample space of a probability experiment and let E denote an event. The complement of E, denoted EC, is the set of all outcomes in the sample space S that are not outcomes in the event E.
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| State the Complement Rule. | If E represents any event and EC represents the complement of E, then P(EC) = 1 – P(E)
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| What do we mean by "Independent" events? | Two events E and F are independent if the occurrence of event E in a probability experiment does not affect the probability of event F.
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| What do we mean by "dependent" events? | Two events are dependent if the occurrence of event E in a probability experiment affects the probability of event F.
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| What is the notation for conditional probability and what does it mean? | The notation P(F | E) is read “the probability of event F given event E”. It is the probability of an event F given the occurrence of the event E.
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| Give the formula for computing conditional probability. | P(F | E) = P(E and F)/P(E) or P(F | E) = N(E and F)/N(E)
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| What is the Multiplication Rule for DEPENDENT events? | P(E and F) = P(E) ∙ P(F | E)
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| What is the Multiplication Rule for INDEPENDENT events? | P(E and F) = P(E) ∙ P(F)
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