If $A$ and $B$ are two events such that $A \subset B$ and $P (B) \neq 0$ , then which of the following is correct?

P (A | B) = 1

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P (A | B) = \frac{P (B)}{P (A)}

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P (A | B) \leq P (A)

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P (A | B) \geq P (A)

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Solution

The correct option is C $P (A | B) \leq P (A)$
$P (A | B) = \frac{P (A \cap B)}{P (B)} = \frac{P (A)}{P (B)} ∵ P (B) \leq 1 ∴ P (A | B) \leq P (A)$

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Similar questions

If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct?

D. None of these

Q. If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then (A) P (B|A) = 1 (B) P (A|B) = 1 (C) P (B|A) = 0 (D) P (A|B) = 0

Q. Let

A

and

B

be two non-null events such that

A \subset B .

Then, which of the following statements is always correct?

If A and B are two events such that A $\subset$ B and P(B) $\neq$ 0, then which of the following is correct?

$(a) P (\frac{A}{B}) = \frac{P (A)}{P (B)} (b) P (\frac{A}{B}) < P (A) (c) P (\frac{A}{B}) \geq P (A) (d) N o n e o f t h e s e$

IF A and B are any two events such that P(A) + P(B) - P (A and B ) = P(A), then
(a) $P (\frac{B}{A}) = 1$
(b) $P (\frac{A}{B}) = 1$
(c) $P (\frac{B}{A}) = 0$
(d) $P (\frac{A}{B}) = 0$

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If A and B are two events such that A⊂B and P(B)≠0, then which of the following is correct?

The correct option is C P(A|B)≤P(A)P(A|B)=P(A∩B)P(B)=P(A)P(B)∵P(B)≤1∴P(A|B)≤P(A)

If $A$ and $B$ are two events such that $A \subset B$ and $P (B) \neq 0$ , then which of the following is correct?

The correct option is C $P (A | B) \leq P (A)$
$P (A | B) = \frac{P (A \cap B)}{P (B)} = \frac{P (A)}{P (B)} ∵ P (B) \leq 1 ∴ P (A | B) \leq P (A)$