When the occurrence of one event has no effect on the probability that another event will occur?
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Probability and Statistics for Engineering and the Sciences8th EditionJay L. Devore 1,232 solutions Two events wherein the occurrence of one event does not affect the occurrence of another event or events What are Independent Events?In statistics and probability theory, independent events are two events wherein the occurrence of one event does not affect the occurrence of another event or events. The simplest example of such events is tossing two coins. The outcome of tossing the first coin cannot influence the outcome of tossing the second coin. Independent events are frequently confused with mutually exclusive events. However, they are two distinct concepts. Mutually exclusive events are events that cannot occur simultaneously. The concept of independent events is not related to the simultaneous occurrence of the events, but it is only concerned with the influence of the occurrence of one event on another. Independent Events and Conditional ProbabilityRemember that conditional probability is the probability of an event A occurring given that event B has already occurred. If two events are independent, the probabilities of their outcomes are not dependent on each other. Therefore, the conditional probability of two independent events A and B is: The equation above may be considered as a definition of independent events. If the equation is violated, the two events are not independent. Probability Rules for Independent EventsIndependent events follow some of the most fundamental probability rules. Some of them include: 1. Rule of MultiplicationThe rule of multiplication is used when we want to find the probability of events occurring simultaneously (it is also known as the joint probability of independent events). The rule of multiplication states the following: In other words, if you want to find the probability of both events A and B taking place, you should multiply the individual probabilities of the two events. 2. Rule of AdditionThe rule of addition allows determining the probability that at least one of the events occurs (it is also known as the union of events). The rule of addition is denoted: The probability of either of events A and B taking place is found by finding the sum of the individual probabilities of both events and subtracting the joint probability of the two events. More ResourcesCFI is the official provider of the Business Intelligence & Data Analyst (BIDA)® certification program, designed to transform anyone into a world-class financial analyst. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional CFI resources below:
When the occurrence of one event does not affect the probability of occurrence of another event is known as?If the probability of occurrence of an event is 0, such an event is called an impossible event and if the probability of occurrence of an event is 1, it is called a sure event.
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?What are Independent Events? In statistics and probability theory, independent events are two events wherein the occurrence of one event does not affect the occurrence of another event or events. The simplest example of such events is tossing two coins.
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.
What do you call events that do not affect the probability of each other?Independent events do not affect one another and do not increase or decrease the probability of another event happening.
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