ProbabilityMedium
Question
For two given events A and B, P(A ∩ B) is
Options
A.not less that P(A) + P(B) - 1
B.not greater than P(A) + P(B)
C.equal to P(A) + P(B) - P(A ∪ B)
D.equal to P(A) + P(B) + P(A ∪ B)
Solution
We know that,
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Also, P(A ∪ B) ≤ 1
∴ P(A ∩ B)max = 1
⇒ P(A ∩ B) ≥ P(A) + P(B) - 1
∴ Option (a) is true.
Again, P(A ∪ B) ≥ 0
∴ P(A ∩ B)max, when P(A ∪ B)max, = 0
⇒ P(A ∩ B) ≤ P(A) + P(B)
∴ Option (b) is true.
Also, P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Thus, (c) is also correct.
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Also, P(A ∪ B) ≤ 1
∴ P(A ∩ B)max = 1
⇒ P(A ∩ B) ≥ P(A) + P(B) - 1
∴ Option (a) is true.
Again, P(A ∪ B) ≥ 0
∴ P(A ∩ B)max, when P(A ∪ B)max, = 0
⇒ P(A ∩ B) ≤ P(A) + P(B)
∴ Option (b) is true.
Also, P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Thus, (c) is also correct.
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