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In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B are
- a)independent
- b)mutually exclusive
- c)mutually exhaustive
- d)dependent
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B ar...
Explanation:
Given probabilities:
- P(A∪B) = 5/6
- P(A) = 5/6
- P(B) = 2/3
Definition of mutually exclusive events:
- Events A and B are mutually exclusive if they cannot occur together, i.e., P(A∩B) = 0.
Calculation of P(A∩B):
- Using the formula P(A∪B) = P(A) + P(B) - P(A∩B), we can find P(A∩B).
- Substituting the given values, we get 5/6 = 5/6 + 2/3 - P(A∩B).
- Solving this equation, we find P(A∩B) = 2/3.
Conclusion:
- Since P(A∩B) is not equal to 0, events A and B are not mutually exclusive.
- Therefore, the correct answer is option 'B' - mutually exclusive.
Given probabilities:
- P(A∪B) = 5/6
- P(A) = 5/6
- P(B) = 2/3
Definition of mutually exclusive events:
- Events A and B are mutually exclusive if they cannot occur together, i.e., P(A∩B) = 0.
Calculation of P(A∩B):
- Using the formula P(A∪B) = P(A) + P(B) - P(A∩B), we can find P(A∩B).
- Substituting the given values, we get 5/6 = 5/6 + 2/3 - P(A∩B).
- Solving this equation, we find P(A∩B) = 2/3.
Conclusion:
- Since P(A∩B) is not equal to 0, events A and B are not mutually exclusive.
- Therefore, the correct answer is option 'B' - mutually exclusive.
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In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B area)independentb)mutually exclusivec)mutually exhaustived)dependentCorrect answer is option 'B'. Can you explain this answer?
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