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# Distinguish between independence of events and mutual exclusivity of events with the help of example

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> Distinguish between independence of events and mutual exclusivity of > events with the help of example --Mutual exclusivity means if one event(A) has happened, then the other event(B) did not happen for sure. It mathematically translates into : P(A|B) = P(B|A) = 0. --Two events are mutually exclusive if they can't both happen. --Independent events are events where knowledge of the probability of one doesn't change the probability of the other.. --They are, in a sense, completely opposite features. If AA and BB are independent, knowledge that AA occurred does not change the probabilities that BB may have occurred. Where as if AA and BB are disjoint, knowledge that AA occurred completely changes the probabilities that BB may have occurred by collapsing them to 00. --Events are mutually exclusive if the occurrence of one event excludes the occurrence of the other(s). Mutually exclusive events cannot happen at the same time. --Mutually exclusive event :- two events are mutually exclusive event when they cannot occur at the same time. e.g if we flip a coin it can only show a head OR a tail, not both. Independent event :- the occurrence of one event does not effect the occurrence of the others e.g if we flip a coin two times, the first time may show a head, but the next time when we flip the coin the outcome will be heads also. From this example we can see the first event does not affect the occurrence of the next event.

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The difference between independence of events and mutual exclusivity events are very simple. The two events are not occur in same time. The independence of events where knowledge of the probability of one doesn't change the probability of the other. and the mutual exclusivity of events are if one events has happened,then the other event did not have happen for sure. You can translated the difference of independence of events and mutual exclusivity of events in mathematically That is, in independence of events can translated into: P(A/B)=P(B/A)=0 and Mutual Exclusivity events can translated into: P(A/B)=P(A) We can take a simple example in find the difference between independence of events and mutual exclusivity events. A = The roll of a die is odd. B = The roll of a die is even. Clearly, the roll of a die must result in a number that is either odd or even; it can't be both. Therefore, events A and B are mutually exclusive. Another example for independence of events are, we can take this in the coin-flipping experiment, event A is defined as the event that the first flip is a head, and event B is defined as the event that the second flip is a head. In other words: : A = {HH, HT} B = {HH, TH}

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