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If A and B are two events of sample space S, then
- a)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0
- b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0
- c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0
- d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If A and B are two events of sample space S, thena)P(A ∩ ...
The probability of occurrence of event A under the condition that event B has already occurred& P(B)≠0 is called Conditional probability i.e; P(A|B)=P(A ∩ B)/P(B). Multiply with P(B) on both sides implies P(A ∩ B)=P(B).P(A|B). So option 'A' is correct.
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If A and B are two events of sample space S, thena)P(A ∩ ...
Explanation:
In probability theory, the probability of two events A and B occurring together is denoted as P(A ∩ B) or P(A ∪ B), depending on whether we are considering the intersection or union of the events.
In this question, we are given two events A and B from a sample space S. We need to determine the correct relationship between P(A ∩ B) and the conditional probability P(A/B).
Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A/B), which is read as "the probability of A given B". The conditional probability of A given B is calculated as the ratio of the probability of A and B occurring together (P(A ∩ B)) to the probability of B occurring (P(B)).
Answer:
The correct answer to this question is option 'A'.
Explanation:
P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0
Reasoning:
To understand why option 'A' is correct, let's break down the equation P(A ∩ B) = P(B)P(A/B) and analyze each part:
1. P(A ∩ B): This represents the probability of events A and B occurring together, i.e., the intersection of A and B.
2. P(B): This represents the probability of event B occurring.
3. P(A/B): This represents the conditional probability of event A given that event B has already occurred.
Explanation of the equation:
The equation P(A ∩ B) = P(B)P(A/B) states that the probability of events A and B occurring together is equal to the product of the probability of event B occurring and the conditional probability of event A given that event B has occurred.
This equation is derived from the definition of conditional probability. When we calculate the conditional probability P(A/B), we divide the probability of A and B occurring together (P(A ∩ B)) by the probability of event B occurring (P(B)). Therefore, the equation P(A ∩ B) = P(B)P(A/B) holds true.
Conclusion:
The correct relationship between P(A ∩ B) and P(A/B) is given by option 'A' - P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0. This equation represents the fundamental relationship between the intersection of two events and the conditional probability.
In probability theory, the probability of two events A and B occurring together is denoted as P(A ∩ B) or P(A ∪ B), depending on whether we are considering the intersection or union of the events.
In this question, we are given two events A and B from a sample space S. We need to determine the correct relationship between P(A ∩ B) and the conditional probability P(A/B).
Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A/B), which is read as "the probability of A given B". The conditional probability of A given B is calculated as the ratio of the probability of A and B occurring together (P(A ∩ B)) to the probability of B occurring (P(B)).
Answer:
The correct answer to this question is option 'A'.
Explanation:
P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0
Reasoning:
To understand why option 'A' is correct, let's break down the equation P(A ∩ B) = P(B)P(A/B) and analyze each part:
1. P(A ∩ B): This represents the probability of events A and B occurring together, i.e., the intersection of A and B.
2. P(B): This represents the probability of event B occurring.
3. P(A/B): This represents the conditional probability of event A given that event B has already occurred.
Explanation of the equation:
The equation P(A ∩ B) = P(B)P(A/B) states that the probability of events A and B occurring together is equal to the product of the probability of event B occurring and the conditional probability of event A given that event B has occurred.
This equation is derived from the definition of conditional probability. When we calculate the conditional probability P(A/B), we divide the probability of A and B occurring together (P(A ∩ B)) by the probability of event B occurring (P(B)). Therefore, the equation P(A ∩ B) = P(B)P(A/B) holds true.
Conclusion:
The correct relationship between P(A ∩ B) and P(A/B) is given by option 'A' - P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0. This equation represents the fundamental relationship between the intersection of two events and the conditional probability.
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If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. Can you explain this answer?
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If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. 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 If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. Can you explain this answer?.
If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. 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 If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two events of sample space S, thena)P(A ∩ B) = P(B)P(A/B); P(B) ≠ 0b)P(A ∪ B) = P(A)P(A/B); P(B) ≠ 0c)P(A ∪ B) = P(B)P(A/B); P(B) ≠ 0d)P(A ∩ B) = P(A)P(A/B); P(B) ≠ 0Correct answer is option 'A'. Can you explain this answer?.
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