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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A) : The probability of an impossible event is 1.
Reason (R) : If A is a perfect subset of B and P(A) < p(b),="" then="" p(b="" –="" a)="" is="" equal="" to="" p(b)="" –="" />
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false but R is True
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion (A) is wrong.
If the probability of an event is 0, then it is called an impossible event.
But Reason (R) is correct.
From Basic Theorem of Probability, P(B – A) = P(B) – P(A), this is true only if the condition given in the question is true.
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Direction: In the following questions, A statement of Assertion (A) i...
Assertion and Reasoning
Assertion (A): The probability of an impossible event is 1.
Reasoning (R): If A is a perfect subset of B and P(A) = 0, then P(B) = 0.
Explanation
An event is impossible if its probability is 0. On the other hand, if the probability of an event is 1, then it is certain to happen. Hence, the probability of an impossible event is 0, and the probability of a certain event is 1.
Now, let us consider the reasoning given in the statement. If A is a perfect subset of B, it means that all the elements of A are also elements of B. In other words, A is a subset of B, and there are no elements in B that are not in A.
If P(A) = 0, it means that the probability of any event in A happening is 0. Since A is a subset of B, the probability of any event in B happening is at most 0 (because all events in A are also in B). Hence, the probability of B is also 0.
Therefore, we can conclude that the reasoning given in the statement is true. However, it does not provide an explanation for why the probability of an impossible event is 1. In fact, the two statements are not directly related. The assertion is a general principle of probability, while the reasoning is a specific mathematical fact about subsets.
Conclusion
In conclusion, the correct answer is option D: A is false but R is true. The probability of an impossible event is 0, not 1. However, the reasoning given in the statement is true and provides a useful fact about subsets and probabilities.
Assertion (A): The probability of an impossible event is 1.
Reasoning (R): If A is a perfect subset of B and P(A) = 0, then P(B) = 0.
Explanation
An event is impossible if its probability is 0. On the other hand, if the probability of an event is 1, then it is certain to happen. Hence, the probability of an impossible event is 0, and the probability of a certain event is 1.
Now, let us consider the reasoning given in the statement. If A is a perfect subset of B, it means that all the elements of A are also elements of B. In other words, A is a subset of B, and there are no elements in B that are not in A.
If P(A) = 0, it means that the probability of any event in A happening is 0. Since A is a subset of B, the probability of any event in B happening is at most 0 (because all events in A are also in B). Hence, the probability of B is also 0.
Therefore, we can conclude that the reasoning given in the statement is true. However, it does not provide an explanation for why the probability of an impossible event is 1. In fact, the two statements are not directly related. The assertion is a general principle of probability, while the reasoning is a specific mathematical fact about subsets.
Conclusion
In conclusion, the correct answer is option D: A is false but R is true. The probability of an impossible event is 0, not 1. However, the reasoning given in the statement is true and provides a useful fact about subsets and probabilities.
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A) : The probability of an impossible event is 1.Reason (R) : If A is a perfect subset of B and P(A) a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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