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If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……
- a)0.1
- b)0.5
- c)0.36
- d)0.2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|...
Given, P(A)=0.3, P(B)=0.9, P(B|A)=0.6,
We know that P(B|A)=P(A ∩ B)/P(A) implies P(A ∩ B)=P(B|A).P(A)
Therefore, P(A ∩ B)=0.6*0.3=0.18. Now P(A|B)=P(A ∩ B)/P(B) implies P(A|B)=0.18/0.9=0.2. So, Correct option is 'D' .
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If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|...
To find the probability of event A given event B, we can use Bayes' theorem which states:
P(A|B) = (P(B|A) * P(A)) / P(B)
Given:
P(A) = 0.3
P(B) = 0.9
P(B|A) = 0.6
Let's substitute these values into Bayes' theorem to find P(A|B):
P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (0.6 * 0.3) / 0.9
P(A|B) = 0.18 / 0.9
P(A|B) = 0.2
Therefore, the probability of event A given event B, P(A|B), is 0.2 or 20%.
Explanation:
To understand why the correct answer is 0.2, let's break down the problem and analyze the given information:
1. P(A) = 0.3
This tells us the probability of event A occurring independently.
2. P(B) = 0.9
This tells us the probability of event B occurring independently.
3. P(B|A) = 0.6
This tells us the probability of event B occurring given that event A has already occurred.
To find P(A|B), we need to determine the probability of event A occurring given that event B has already occurred. This can be calculated using Bayes' theorem.
Bayes' theorem states that the probability of event A given event B is equal to the probability of event B given event A multiplied by the probability of event A, divided by the probability of event B.
In this case, we have P(B|A), P(A), and P(B), so we can substitute these values into Bayes' theorem to find P(A|B).
After substituting the given values, we get:
P(A|B) = (0.6 * 0.3) / 0.9
P(A|B) = 0.18 / 0.9
P(A|B) = 0.2
Therefore, the probability of event A given event B, P(A|B), is 0.2 or 20%.
The correct answer is option D) 0.2.
P(A|B) = (P(B|A) * P(A)) / P(B)
Given:
P(A) = 0.3
P(B) = 0.9
P(B|A) = 0.6
Let's substitute these values into Bayes' theorem to find P(A|B):
P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (0.6 * 0.3) / 0.9
P(A|B) = 0.18 / 0.9
P(A|B) = 0.2
Therefore, the probability of event A given event B, P(A|B), is 0.2 or 20%.
Explanation:
To understand why the correct answer is 0.2, let's break down the problem and analyze the given information:
1. P(A) = 0.3
This tells us the probability of event A occurring independently.
2. P(B) = 0.9
This tells us the probability of event B occurring independently.
3. P(B|A) = 0.6
This tells us the probability of event B occurring given that event A has already occurred.
To find P(A|B), we need to determine the probability of event A occurring given that event B has already occurred. This can be calculated using Bayes' theorem.
Bayes' theorem states that the probability of event A given event B is equal to the probability of event B given event A multiplied by the probability of event A, divided by the probability of event B.
In this case, we have P(B|A), P(A), and P(B), so we can substitute these values into Bayes' theorem to find P(A|B).
After substituting the given values, we get:
P(A|B) = (0.6 * 0.3) / 0.9
P(A|B) = 0.18 / 0.9
P(A|B) = 0.2
Therefore, the probability of event A given event B, P(A|B), is 0.2 or 20%.
The correct answer is option D) 0.2.
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If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct answer is option 'D'. Can you explain this answer?
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If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct 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 If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct 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 If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct answer is option 'D'. Can you explain this answer?.
If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct 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 If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct 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 If A and B are two events such that P(A) = 0.3 and P(B) = 0.9 and P(B|A) = 0.6,then P(A|B) = ……a)0.1b)0.5c)0.36d)0.2Correct answer is option 'D'. Can you explain this answer?.
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