When the occurrence of one event has no effect on the probability of the occurrence of another event the event are called?
DefinitionsProbability ExperimentProcess which leads to well-defined results call outcomesOutcomeThe result of a single trial of a probability experimentSample SpaceSet of all possible outcomes of a probability experimentEventOne or more outcomes of a probability experimentClassical ProbabilityUses the sample space to determine the numerical probability that an event will happen. Also called theoretical probability.Equally Likely EventsEvents which have the same probability of occurring.Complement of an EventAll the events in the sample space except the given events.Empirical ProbabilityUses a frequency distribution to determine the numerical probability. An empirical probability is a relative frequency.Subjective ProbabilityUses probability values based on an educated guess or estimate. It employs opinions and inexact information.Mutually Exclusive EventsTwo events which cannot happen at the same time.Disjoint EventsAnother name for mutually exclusive events.Independent EventsTwo events are independent if the occurrence of one does not affect the probability of the other occurring.Dependent EventsTwo events are dependent if the first event affects the outcome or occurrence of the second event in a way the probability is changed.Conditional ProbabilityThe probability of an event occurring given that another event has already occurred.Bayes' TheoremA formula which allows one to find the probability that an event occurred as the result of a particular previous event.Table of Contents If you enjoy this section, take a Finite or Statistics course. Take a Finite or Statistics course even if you don't enjoy this section, they're loads of fun. Show
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DefinitionsExperimentAny happening whose result is uncertain.OutcomesPossible results from an experimentSample SpaceSet of all possible outcomesEventSubset of the sample space. One or more outcomes.Equally Likely EventsEvents which have the same chance of occurringProbabilityChance that an event will occur. Theoretically for equally likely events, it is the number of ways an event can occur divided by number of outcomes in the sample space. Empirically, the long term relative frequency.Independent EventsEvents in which the occurrence of one event does not change the probability of the occurrence of the other. One does not affect the other.Dependent EventsEvents that are not independent.Mutually Exclusive EventsEvents that can not happen at the same time. Disjoint events.All Inclusive EventsEvents whose union comprises the totality of the sample space.Complementary EventsTwo mutually exclusive events that are all inclusive.Sample SpacesThe sample space is the set of all the possible outcomes in an experiment and is denoted by a capital letter S. If you were to roll a single die, then S = { 1, 2, 3, 4, 5, 6 }, the set of all possible outcomes. If you were to roll two dice and look at the sum of the two dice, then S = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }. Equally Likely EventsHowever, not all sample spaces are created equally. In fact, that last example is not. There is only one way that a sum of 2 can be rolled, a 1 on the first die and a 1 on the second die. There are four ways that a sum of five can be rolled: 1-4, 2-3, 3-2, 4-1 (don't be confused here, 1-4 is a 1 on the first die and a 4 on the second and is different than a 4 on the first and a 1 on the second. If it helps, pretend that you're rolling one die and a friend is rolling the other). We want our sample spaces to be equally likely if at all possible. Classical / Theoretical ProbabilityIf outcomes are equally likely, then the probability of an event occurring is the number in the event divided by the number in the sample space. P(E) = n(E) / n(S) The probability of rolling a six on a single roll of a die is 1/6 because there is only 1 way to roll a six out of 6 ways it could be rolled. The probability of getting a sum of 5 when rolling two dice is 4/36 = 1/9 because there are 4 ways to get a five and there are 36 ways to roll the dice (Fundamental Counting Principle - 6 ways to roll the first times 6 ways to roll the second). Do not make the mistake of saying that the probability of rolling a sum of 5 is 1/11 because there is one 5 out of a sample space of 11 sums (2 through 12). When the sample spaces are not equally likely, do not divide by the number in the sample space. Properties of Probabilities
Addition RulesWhen you want to find the probability of one event OR another occurring, you add their probabilities together. This can lead to problems however, if they have something in common. The probability of one or both of two events occurring is ... P(A or B) = P(A) + P(B) - P(A and B) Mutually Exclusive EventsMutually Exclusive Events have nothing in common. The intersection of the two events is the empty set. The probability of A and B both occurring is 0 because they can't occur at the same time. If two events are mutually exclusive, then the probability of one or the other occurring is ... P(A or B) = P(A) + P(B) Multiplication RulesWhen you want to find the probability of two events both occurring, then you need to apply the Fundamental Counting Principle. This principle can be extended to probabilities. Independent EventsIndependent Events are events where one occurring doesn't change the probability of the other occurring. When events are independent, the probability of them both occurring is ... P(A and B) = P(A) * P(B) We don't have time to get into probability very deeply. If we did, we would cover conditional probability - the probability of dependent events. Complementary EventsThe root word in complementary is "complete". Complementary events complete, or make whole. Complementary events are mutually exclusive, but when combined make the entire sample space. The symbol for the complement of event A is A'. Some books will put a bar over the set to indicate its complement. Since complementary events are mutually exclusive, we can use the special addition rule to find its probability. Furthermore, complementary events are all inclusive, so they make the sample space when combined, so their probabilities have a sum of 1. The sum of the probabilities of complementary events is 1. P(A) + P(A') = 1 When the occurrence of one event has no effect on the occurrence of the other?If the occurrence of one event has no effect on the likelihood of another event, the two events are said to be independent. What are two events called when the occurrence of one event does not affect the occurrence of the other event?Two events are independent if the occurrence of one does not affect the probability of the other occurring. When the occurrence of one event has effect on the probability of the occurrence of another event the events are called?Dependent events in probability are events whose occurrence of one affects the probability of occurrence of the other. Suppose a bag has 3 red and 6 green balls. When the occurrence of some event has no effect on the probability of occurrence of some other event the two events are said to be statistically independent?Mutually Exclusive Events are when the occurrence of one event has no effect on the probability of occurrence of the other. When the occurrence of one event has no effect on the probability of the occurrence of another event the events are?If the occurrence of any event is completely unaffected by the occurrence of any other event, such events are known as an independent event in probability and the events which are affected by other events are known as dependent events.
When the occurrence of one event has no effect on the probability of the occurrence of another event are the independent B dependent C mutually exclusive equally likely?Mutually exclusive events occur when two or more things happen at the same time. Independent events occur when the occurrence of one event has no bearing on the occurrence of another. The occurrence of one event will result in the non-occurrence of the other in mutually exclusive events.
When the occurrence of some event has no effect on the probability of occurrence of some other event the two events are said to be statistically independent?If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events. P(A) = P(A│B) = 1/2 , which implies that the occurrence of event B has not affected the probability of occurrence of the event A .
When the occurrence of one has no effect on the occurrence of the other?Two events are independent IF the occurrence of one event has NO effect on the probability that the second event will occur.
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