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The events in an experiment are mutually exclusive if only one can occur at a time true or false?
provide one business-related example each, with explanation, for mutually exclusive and independent events
What does the expression mutually exclusive mean?
Mutually exclusive means if one thing is true the other must be false and vice versa.If A is true, B is false. If B is true, A is false.For instance,The ball was totally red.The ball was totally blue.These are mutually exclusive because the ball can only be one or the other.The ball was red.The ball was blue.These are NOT mutually exclusive because the ball could also be red AND blue.
Two events are mutually exclusive if the occurrence of one depends on the occurrence of the other?
That depends on your definition of "depends." Mutually exclusive events are events that cannot occur at the same time. If you knew that Independent events most certainly can happen at the same time, you could easily deduce that mutually exclusive events are always dependent events. And while it's true dependent events affect the outcome of one another, that's not so easy to see when your dealing with events that don't occur in succession.It can be said that if a mutually exclusive event occurs, the other events that are mutually exclusive in relation to it have not taken place, i.e. the complement of that event has not taken place. When you look at only two events that are mutually exclusive and jointly exhaustive (i.e. all the possible events) like flipping a coin once and getting either a head or a tails (where the probability of the coin landing on it's side is 0), you can say that one event, flipping a head, is dependent on the other event, flipping a tail, not happening. Therefore the events are mutually exclusive.Now imagine two events which are still mutually exclusive but not jointly exhaustive, e.g. rolling a 2 or a 3 with a six sided die. Lets assume the die is not weighted so the probability of each is 1/6. A roll of two does not only depend on not rolling a three. To roll a 2 means not rolling a 1,3,4,5 or 6. To say that rolling a 2 and rolling a 3 are mutually exclusive if the occurrence one depends on the occurrence of the other is ambiguous at best, if not wrong. Rolling a 2 and rolling a 3 are mutually exclusive only because its impossible for both to happen at the same time with one roll, or you can say that P(2and3)=0.It's fair to say that two events are mutually exclusive if the occurrence of one depends on the other not happening. But if you thought that two events are mutually exclusive because the occurrence of one relays on the occurrence of the other then you were wrong. That just describes dependent events in succession.If one event's occurence depends upon the occurence of another, and the events cannot occur with a certain outcome otherwise, they are said to be dependent events. Mutually exclusive events are events that cannot occur together, as the occurence of one prohibits the occurence of the other. An example of a mutually exclusive event is this: two dice are rolled; what is the possibility of rolling both a nine and a double? One cannot roll both a nine and a double simultaneously; therefore, the events are mutually exclusive because one outcome excludes the other. An example of a dependent event is this: Susan is baking cookies. She has enough batter for two dozen chocolate chip cookies and one dozen oatmeal cookies. Therefore, the ratio of chocolate chip to oatmeal is 1.5:1. If Susan's little brother eats half of the chocolate chip cookies, the ratio changes to become 1:1. The possibility of the ratio being 1:1 is dependent upon Susan's brother eating half of the chocolate chip cookies. Thus, it is a dependent event. If one event's occurence depends upon the occurence of another, and the events cannot occur with a certain outcome otherwise, they are said to be dependent events. Mutually exclusive events are events that cannotoccur together, as the occurence of one prohibits the occurence of the other. An example of a mutually exclusive event is this: two dice are rolled; what is the possibility of rolling both a nine and a double? One cannot roll both a nine and a double simultaneously; therefore, the events are mutually exclusive because one outcome excludes the other. An example of a dependent event is this: Susan is baking cookies. She has enough batter for two dozen chocolate chip cookies and one dozen oatmeal cookies. Therefore, the ratio of chocolate chip to oatmeal is 1.5:1. If Susan's little brother eats half of the chocolate chip cookies, the ratio changes to become 1:1. The possibility of the ratio being 1:1 is dependent upon Susan's brother eating half of the chocolate chip cookies. Thus, it is a dependent event. If one event's occurence depends upon the occurence of another, and the events cannot occur with a certain outcome otherwise, they are said to be dependent events. Mutually exclusive events are events that cannotoccur together, as the occurence of one prohibits the occurence of the other. An example of a mutually exclusive event is this: two dice are rolled; what is the possibility of rolling both a nine and a double? One cannot roll both a nine and a double simultaneously; therefore, the events are mutually exclusive because one outcome excludes the other. An example of a dependent event is this: Susan is baking cookies. She has enough batter for two dozen chocolate chip cookies and one dozen oatmeal cookies. Therefore, the ratio of chocolate chip to oatmeal is 1.5:1. If Susan's little brother eats half of the chocolate chip cookies, the ratio changes to become 1:1. The possibility of the ratio being 1:1 is dependent upon Susan's brother eating half of the chocolate chip cookies. Thus, it is a dependent event.Mutually exclusive events refers to the events that cannot occur at the same time.
What is mutual exclusive in theology?
It's more of a philosophical term in general. It refers to two or more conditions which can't be true at the same time. For instance, the statements "There is a god." and "There is no god." are mutually exclusive.
Is it true that the probability of the union of two events id the sum of the probabilities of those events?
yes P(AUB)=P(A)+P(B) but only for mutualy exclusive events
