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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?
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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.
Most Upvoted Answer
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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