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Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :
- a)Mutually exclusive (1979)
- b)Independent and mutually exclusive
- c)Dependent
- d)None of these.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two fair dice are tossed. Let x be the event that the first die shows ...
The two events can happen simultaneously e.g., (2, 3)
∴ not mutually exclusive.
Also are not dependent on each other.
∴ not mutually exclusive.
Also are not dependent on each other.
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Two fair dice are tossed. Let x be the event that the first die shows ...
Explanation:
Mutually Exclusive Events:
- Two events are mutually exclusive if they cannot occur at the same time.
- In this case, event x (the first die showing an even number) and event y (the second die showing an odd number) can both occur simultaneously.
- Therefore, x and y are not mutually exclusive.
Independent Events:
- Two events are independent if the occurrence of one event does not affect the occurrence of the other event.
- In this case, the outcome of the first die does not affect the outcome of the second die, so x and y are independent events.
Dependent Events:
- Two events are dependent if the occurrence of one event affects the occurrence of the other event.
- In this case, the outcome of the first die could potentially influence the outcome of the second die (for example, if the first die shows a 6, the probability of the second die being odd changes).
- Therefore, x and y are dependent events.
Conclusion:
- Since the events x and y are not mutually exclusive and are dependent on each other, the correct answer is option 'D' - None of these.
Mutually Exclusive Events:
- Two events are mutually exclusive if they cannot occur at the same time.
- In this case, event x (the first die showing an even number) and event y (the second die showing an odd number) can both occur simultaneously.
- Therefore, x and y are not mutually exclusive.
Independent Events:
- Two events are independent if the occurrence of one event does not affect the occurrence of the other event.
- In this case, the outcome of the first die does not affect the outcome of the second die, so x and y are independent events.
Dependent Events:
- Two events are dependent if the occurrence of one event affects the occurrence of the other event.
- In this case, the outcome of the first die could potentially influence the outcome of the second die (for example, if the first die shows a 6, the probability of the second die being odd changes).
- Therefore, x and y are dependent events.
Conclusion:
- Since the events x and y are not mutually exclusive and are dependent on each other, the correct answer is option 'D' - None of these.
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Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. Can you explain this answer?
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Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. 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 Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. Can you explain this answer?.
Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. 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 Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two fair dice are tossed. Let x be the event that the first die shows an even number and y be the event that the second die shows an odd number. The two events x and y are :a)Mutually exclusive (1979)b)Independent and mutually exclusivec)Dependentd)None of these.Correct answer is option 'D'. Can you explain this answer?.
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