CA Foundation Exam > CA Foundation Questions > If P(A/B) = P(A), thena)A is independent of B...
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If P(A/B) = P(A), then
- a)A is independent of B
- b)B is independent of A
- c)B is dependent of A
- d)Both (a) and (b)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)...
Explanation:
The given statement P(A/B) = P(A) can be rewritten as P(A ∩ B) = P(A)P(B).
If P(A/B) = P(A), then it means that the occurrence of event B does not affect the probability of event A. This can happen only if events A and B are independent of each other.
Therefore, the correct answer is option D, i.e. A is independent of B and B is independent of A.
In other words, if P(A/B) = P(A), then:
- Event A and event B are independent of each other.
- The occurrence of event B does not affect the probability of event A, and vice versa.
- The probability of A given B is equal to the probability of A, and vice versa.
The given statement P(A/B) = P(A) can be rewritten as P(A ∩ B) = P(A)P(B).
If P(A/B) = P(A), then it means that the occurrence of event B does not affect the probability of event A. This can happen only if events A and B are independent of each other.
Therefore, the correct answer is option D, i.e. A is independent of B and B is independent of A.
In other words, if P(A/B) = P(A), then:
- Event A and event B are independent of each other.
- The occurrence of event B does not affect the probability of event A, and vice versa.
- The probability of A given B is equal to the probability of A, and vice versa.
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Community Answer
If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)...
P(a/b)=p(A intersection B)/p(B)
if A and B are independent P(A intersec B)=P(A)×P(B)
P(a/b)=P(A)×P(B)/P(B)
=P(A)
if A and B are independent P(A intersec B)=P(A)×P(B)
P(a/b)=P(A)×P(B)/P(B)
=P(A)
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If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer?
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If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer?.
If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P(A/B) = P(A), thena)A is independent of Bb)B is independent of Ac)B is dependent of Ad)Both (a) and (b)Correct answer is option 'D'. Can you explain this answer?.
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