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When the sets A and B are two events associated with a sample space, then "A ∩ B " is the event common to
- a)Either A or B or both
- b)Only one of the two, A or B
- c)Both A and B
- d)Neither A nor B
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
When the sets A and B are two events associated with a sample space, t...
Understanding Events A and B
In probability theory, events are subsets of a sample space. When we talk about two events A and B, we can analyze their relationship through various operations, one of which is the intersection denoted by "A ∩ B".
What is A ∩ B?
- The intersection "A ∩ B" refers to the set of outcomes that are common to both events A and B.
- This means that for an outcome to be part of "A ∩ B", it must satisfy the conditions of both events simultaneously.
Why is the Correct Answer C?
- The correct answer is option 'C', which states that "A ∩ B" represents outcomes that occur in both events A and B.
- In simpler terms, if you were to visualize events A and B in a Venn diagram, "A ∩ B" would be the overlapping area where both circles intersect.
Clarifying the Other Options
- a) "Either A or B or both" refers to the union of events A and B (A ∪ B), which includes all outcomes in A, B, or both.
- b) "Only one of the two, A or B" suggests a scenario where outcomes belong exclusively to one event, which is not what "A ∩ B" denotes.
- d) "Neither A nor B" indicates outcomes that do not belong to either event, which again does not describe the intersection.
Conclusion
In summary, "A ∩ B" specifically captures the essence of both events occurring together. Therefore, the assertion that "A ∩ B" is the event common to both A and B is accurately represented by option 'C'. Understanding these relationships is fundamental in probability and helps in solving complex problems in the JEE syllabus.
In probability theory, events are subsets of a sample space. When we talk about two events A and B, we can analyze their relationship through various operations, one of which is the intersection denoted by "A ∩ B".
What is A ∩ B?
- The intersection "A ∩ B" refers to the set of outcomes that are common to both events A and B.
- This means that for an outcome to be part of "A ∩ B", it must satisfy the conditions of both events simultaneously.
Why is the Correct Answer C?
- The correct answer is option 'C', which states that "A ∩ B" represents outcomes that occur in both events A and B.
- In simpler terms, if you were to visualize events A and B in a Venn diagram, "A ∩ B" would be the overlapping area where both circles intersect.
Clarifying the Other Options
- a) "Either A or B or both" refers to the union of events A and B (A ∪ B), which includes all outcomes in A, B, or both.
- b) "Only one of the two, A or B" suggests a scenario where outcomes belong exclusively to one event, which is not what "A ∩ B" denotes.
- d) "Neither A nor B" indicates outcomes that do not belong to either event, which again does not describe the intersection.
Conclusion
In summary, "A ∩ B" specifically captures the essence of both events occurring together. Therefore, the assertion that "A ∩ B" is the event common to both A and B is accurately represented by option 'C'. Understanding these relationships is fundamental in probability and helps in solving complex problems in the JEE syllabus.
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When the sets A and B are two events associated with a sample space, t...
Intersection of two sets A ∩ B is the set of those elements which are common to both A and B. i.e., which belong to both ‘A and B’.
If A and B are two events, then the set A ∩ B denotes the event ‘A and B’.
If A and B are two events, then the set A ∩ B denotes the event ‘A and B’.
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When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer?.
When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer?.
Solutions for When the sets A and B are two events associated with a sample space, then "A ∩ B "is the event common toa)Either A or B or bothb)Only one of the two, A or Bc)Both A and Bd)Neither A nor BCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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