If A and B are two events such that A - B and PB-0- then 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 A d None of these

If A⊂ B, then A∩ B=A ∴ PA∩ B=A= P(A) We know that P(A/B) = P (A∩ B)/P(B)= P(A/B) But P(B)≤ 1 ∴ P(A/B)≥ P(A), Hence, C is the correct option. ...

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Standard XII

Mathematics

Conditional Probability

If A and B ar...

Question

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

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

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Solution

If $A \subset B, t h e n A \cap B = A$

$∴$ P $A \cap B = A$ = P(A)

We know that $P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)} = P (\frac{A}{B})$
$B u t P (B) \leq 1 ∴ P (\frac{A}{B}) \geq P (A)$ , Hence, C is the correct option.

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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?

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. If

A

and

B

are two events such that

A \subset B

and

P (B) \neq 0

, then which of the following is correct?

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) $P (\frac{A}{B}) = 0$

Q. If A and B are two events such that P(A/B) = p, P(A) = p,

P (B) = \frac{1}{3} and P (A \cup B) = \frac{5}{9},

then p = _____________.

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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? (a) P(AB)=P(A)P(B) (b) P(AB)<P(A) (c) P(AB)≥P(A) (d) None of these

If A⊂B, then A∩B=A ∴ PA∩B=A= P(A) We know that P(AB)=P(A∩B)P(B)=P(AB) But P(B)≤1∴ P(AB)≥P(A), Hence, C is the correct option.

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 $A \subset B, t h e n A \cap B = A$

$∴$ P $A \cap B = A$ = P(A)

We know that $P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)} = P (\frac{A}{B})$
$B u t P (B) \leq 1 ∴ P (\frac{A}{B}) \geq P (A)$ , Hence, C is the correct option.