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If A, B, C are three mutually exclusive and exhaustive events of a trial such that P(A) = 2P(B) = 3P(C) then P(A) =
- a)1/3
- b)2/5
- c)3/8
- d)6/11
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If A, B, C are three mutually exclusive and exhaustive events of a tri...
Understanding the Problem
In this problem, we have three mutually exclusive and exhaustive events: A, B, and C. The probabilities are related as follows:
- P(A) = 2P(B)
- P(A) = 3P(C)
Setting Up the Equations
Let:
- P(B) = x
- Then, P(A) = 2x (from P(A) = 2P(B))
- And, P(C) = (2/3)P(A) = (2/3)(2x) = (4/3)x (from P(A) = 3P(C))
Using the Total Probability Rule
Since A, B, and C are exhaustive events, we know that:
P(A) + P(B) + P(C) = 1
Substituting the values we have:
2x + x + (4/3)x = 1
Simplifying the Equation
Combine the terms:
(2x + x + (4/3)x) = (3x + (4/3)x) = (9/3)x + (4/3)x = (13/3)x
Setting the equation equal to 1:
(13/3)x = 1
Solving for x
To find x:
x = 3/13
Then, substituting back to find P(A):
P(A) = 2x = 2 * (3/13) = 6/13
Conclusion
The probabilities are:
- P(A) = 6/13
- P(B) = 3/13
- P(C) = 4/13
Thus, the correct answer is option 'D' (6/11) is incorrect; the correct probability for P(A) should actually be 6/13. The calculations show the relationships between the events clearly.
Make sure to verify the given answer options to ensure accuracy.
In this problem, we have three mutually exclusive and exhaustive events: A, B, and C. The probabilities are related as follows:
- P(A) = 2P(B)
- P(A) = 3P(C)
Setting Up the Equations
Let:
- P(B) = x
- Then, P(A) = 2x (from P(A) = 2P(B))
- And, P(C) = (2/3)P(A) = (2/3)(2x) = (4/3)x (from P(A) = 3P(C))
Using the Total Probability Rule
Since A, B, and C are exhaustive events, we know that:
P(A) + P(B) + P(C) = 1
Substituting the values we have:
2x + x + (4/3)x = 1
Simplifying the Equation
Combine the terms:
(2x + x + (4/3)x) = (3x + (4/3)x) = (9/3)x + (4/3)x = (13/3)x
Setting the equation equal to 1:
(13/3)x = 1
Solving for x
To find x:
x = 3/13
Then, substituting back to find P(A):
P(A) = 2x = 2 * (3/13) = 6/13
Conclusion
The probabilities are:
- P(A) = 6/13
- P(B) = 3/13
- P(C) = 4/13
Thus, the correct answer is option 'D' (6/11) is incorrect; the correct probability for P(A) should actually be 6/13. The calculations show the relationships between the events clearly.
Make sure to verify the given answer options to ensure accuracy.
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If A, B, C are three mutually exclusive and exhaustive events of a trial such that P(A) = 2P(B) = 3P(C) then P(A) =a)1/3b)2/5c)3/8d)6/11Correct answer is option 'D'. Can you explain this answer?
Question Description
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If A, B, C are three mutually exclusive and exhaustive events of a trial such that P(A) = 2P(B) = 3P(C) then P(A) =a)1/3b)2/5c)3/8d)6/11Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A, B, C are three mutually exclusive and exhaustive events of a trial such that P(A) = 2P(B) = 3P(C) then P(A) =a)1/3b)2/5c)3/8d)6/11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A, B, C are three mutually exclusive and exhaustive events of a trial such that P(A) = 2P(B) = 3P(C) then P(A) =a)1/3b)2/5c)3/8d)6/11Correct answer is option 'D'. Can you explain this answer?.
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