P (A ∪ B) = P (A ∩ B) if the relation between P (A) and P (B) is :

1.	P (A ∪ B) = P (A ∩ B) if the relation between P (A) and P (B) is : (a) P (A) + P (B) = 2P (A ∪ B) (b) P (A) + P (B) = 2P (A) P (A ⁄ B) (c) P (A) + P (B) = 2P (A) P (B ⁄ A) (d) none of these
Answer» Correct option (c) P (A) + P (B) = 2P (A) P (B ⁄ A) Explanation: We have P (A ∪ B) = P (A) + P (B) − P (A ∩ B) ...(1) Since P (A ∪ B) = P (A ∩ B) [given] P (A ∩ B) = P (A) + P (B) − P (A ∩ B) [from (1)] ⇒ 2P (A ∩ B) = P (A) + P (B) ⇒ P (A) + P (B) = 2P (A ∩ B) ⇒ P (A) + P (B) = 2P (A) P (B ⁄ A).

P (A ∪ B) = P (A ∩ B) if the relation between P (A) and P (B) is : (a) P (A) + P (B) = 2P (A ∪ B) (b) P (A) + P (B) = 2P (A) P (A ⁄ B) (c) P (A) + P (B) = 2P (A) P (B ⁄ A) (d) none of these

Answer»

Correct option (c) P (A) + P (B) = 2P (A) P (B ⁄ A)

Explanation:

We have P (A ∪ B) = P (A) + P (B) − P (A ∩ B) ...(1)

Since P (A ∪ B) = P (A ∩ B) [given]

P (A ∩ B) = P (A) + P (B) − P (A ∩ B) [from (1)]

⇒ 2P (A ∩ B) = P (A) + P (B)

⇒ P (A) + P (B) = 2P (A ∩ B)

⇒ P (A) + P (B) = 2P (A) P (B ⁄ A).

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P (A ∪ B) = P (A ∩ B) if the relation between P (A) and P (B) is : (a) P (A) + P (B) = 2P (A ∪ B) (b) P (A) + P (B) = 2P (A) P (A ⁄ B) (c) P (A) + P (B) = 2P (A) P (B ⁄ A) (d) none of these

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