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If two events A and B are independent, then they can not be mutually exclusive?
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If two events A and B are independent, then they can not be mutually e...
Explanation: Independent and Mutually Exclusive Events
Independent Events
When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the occurrence of the other event. In other words, the probability of both events A and B occurring together is simply the product of their individual probabilities.
Mutually Exclusive Events
On the other hand, when two events A and B are mutually exclusive, it means that they cannot occur at the same time. The occurrence of one event excludes the occurrence of the other event.
Why Can't Independent Events be Mutually Exclusive?
If two events A and B are independent, it means that the occurrence of one event does not affect the probability of the occurrence of the other event. Therefore, it is possible for both events A and B to occur together. On the other hand, if two events A and B are mutually exclusive, it means that they cannot occur at the same time. Therefore, the occurrence of one event affects the probability of the occurrence of the other event, making them dependent on each other.
Example
For example, let's say that event A is flipping a coin and getting heads, and event B is rolling a die and getting a 6. These events are independent because the probability of getting heads on a coin flip does not affect the probability of rolling a 6 on a die roll. However, these events are not mutually exclusive because it is possible to get heads on a coin flip and roll a 6 on a die roll together.
Conclusion
In conclusion, independent events can never be mutually exclusive because the occurrence of one event does not affect the probability of the occurrence of the other event, while mutually exclusive events cannot occur at the same time, making them dependent on each other.
Community Answer
If two events A and B are independent, then they can not be mutually e...
Yeah.
Because Independent means that the happening if 1 event does not affect the happening of the other,
Whereas Mutually exclusive means that the happening if 1 event prevents the happening of the other.
Because Independent means that the happening if 1 event does not affect the happening of the other,
Whereas Mutually exclusive means that the happening if 1 event prevents the happening of the other.
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If two events A and B are independent, then they can not be mutually exclusive? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If two events A and B are independent, then they can not be mutually exclusive? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two events A and B are independent, then they can not be mutually exclusive?.
If two events A and B are independent, then they can not be mutually exclusive? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If two events A and B are independent, then they can not be mutually exclusive? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two events A and B are independent, then they can not be mutually exclusive?.
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