If A and B are two events such that A⊂Band P(B)=0,them which of the following is correct?(A) P(A∣B)=P(A)P(B) (B) P(A∣B)<P(A) (C) P(A∣B)≥P(B) (D) none of these

Solution: As, we are given that A⊂B, it means P(A∩B)=P(A)Then,P(A∣B)=P(B)P(A∩B)=P(B)P(A)so, option A is incorect.Now, we are given that,P(B)=0 means P(B)≤1If P(B)≤1, then it implies,P(A∣B)≥P(A) which is the correct option.

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If A and B are two events such that $A \subset B$ and $P (B) \neq = 0,$ them which of the following is correct?(A) $P (A ∣ B) = \frac{P ( B )}{P ( A )}$ (B) $P (A ∣ B) < P (A)$ (C) $P (A ∣ B) \geq P (B)$ (D) none of these

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If A and B are two events such that

A \subset B

and

P (B) \neq = 0,

them which of the following is correct?(A)

P (A ∣ B) = \frac{P ( B )}{P ( A )}

(B)

P (A ∣ B) < P (A)

(C)

P (A ∣ B) \geq P (B)

(D) none of these

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Text solutionVerified

Solution: As, we are given that

A \subset B

, it means

P (A \cap B) = P (A)

Then,

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )} = \frac{P ( A )}{P ( B )}

so, option A is incorect.
Now, we are given that,

P (B) \neq = 0

means

P (B) \leq 1

P (B) \leq 1

, then it implies,

P (A ∣ B) \geq P (A)

which is the correct option.

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Question Text	If A and B are two events such that $A \subset B$ and $P (B) \neq = 0,$ them which of the following is correct?(A) $P (A ∣ B) = \frac{P ( B )}{P ( A )}$ (B) $P (A ∣ B) < P (A)$ (C) $P (A ∣ B) \geq P (B)$ (D) none of these
Answer Type	Text solution:1
Upvotes	150

If A and B are two events such that A⊂Band P(B)=0,them which of the following is correct?(A) P(A∣B)=P(A)P(B)​ (B) P(A∣B)<P(A) (C) P(A∣B)≥P(B) (D) none of these

Text solutionVerified

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If A and B are two events such that $A \subset B$ and $P (B) \neq = 0,$ them which of the following is correct?(A) $P (A ∣ B) = \frac{P ( B )}{P ( A )}$ (B) $P (A ∣ B) < P (A)$ (C) $P (A ∣ B) \geq P (B)$ (D) none of these