ACT Exam > ACT Questions > If P(A∪ B) = 3/4, P(A ∩ B) = 1/4, P(A...
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If P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, P(A̅ ) = 2/3, then find the value of P(B).
- a)1/3
- b)1
- c)5/3
- d)2/3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If P(A∪ B) = 3/4, P(A ∩ B) = 1/4, P(A ) = 2/3, then find the v...
Concept:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Explanation:
P(A U B) = 3/4,
P(A ∩ B) = 1/4,
P( A̅ ) = 2/3
Since, P(A U B) = P(A) + P(B) - P(A ∩ B)
Most Upvoted Answer
If P(A∪ B) = 3/4, P(A ∩ B) = 1/4, P(A ) = 2/3, then find the v...
Concept:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Explanation:
P(A U B) = 3/4,
P(A ∩ B) = 1/4,
P( A̅ ) = 2/3
Since, P(A U B) = P(A) + P(B) - P(A ∩ B)
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If P(A∪ B) = 3/4, P(A ∩ B) = 1/4, P(A ) = 2/3, then find the v...
Given Information:
- P(A ∪ B) = 3/4
- P(A ∩ B) = 1/4
- P(A) = 2/3
Calculation:
- The formula for finding the probability of the union of two events is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- Substituting the given values, we have:
3/4 = 2/3 + P(B) - 1/4
3/4 = 8/12 + P(B) - 3/12
3/4 = 5/12 + P(B)
- Simplifying further, we get:
P(B) = 3/4 - 5/12
P(B) = 9/12 - 5/12
P(B) = 4/12
P(B) = 1/3
Therefore, the value of P(B) is 1/3.
Therefore, the correct answer is option 'D' 2/3.
- P(A ∪ B) = 3/4
- P(A ∩ B) = 1/4
- P(A) = 2/3
Calculation:
- The formula for finding the probability of the union of two events is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- Substituting the given values, we have:
3/4 = 2/3 + P(B) - 1/4
3/4 = 8/12 + P(B) - 3/12
3/4 = 5/12 + P(B)
- Simplifying further, we get:
P(B) = 3/4 - 5/12
P(B) = 9/12 - 5/12
P(B) = 4/12
P(B) = 1/3
Therefore, the value of P(B) is 1/3.
Therefore, the correct answer is option 'D' 2/3.
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If P(A∪ B) = 3/4, P(A ∩ B) = 1/4, P(A ) = 2/3, then find the value of P(B).a)1/3b)1c)5/3d)2/3Correct answer is option 'D'. Can you explain this answer?
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