If A and B are two events such that PA-0 and PB-A-t- thena A - B b B - Ac B -d A -

Given, P(A) ≠ 0 and P (B/A ) = 1 ⇒ P (B/A ) = P(A ∩ B)/P(A) = 1 ⇒ P(A ∩ B) = P(A) ⇒ A ∩ B = A ⇒ a ⊏ B ...

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Standard XII

Mathematics

Standard Deviation about Mean

If A and B ar...

Question

If A and B are two events such that P (A) $\neq 0$ and

$P (\frac{B}{A}) = t,$ then

(a) $A ⊏ B$ (b) $B ⊏ A$
(c) $B = ϕ$ (d) $A = ϕ$

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Solution

Given, $P (A) \neq 0 a n d P (\frac{B}{A}) = 1 \Rightarrow P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)} = 1 \Rightarrow P (A \cap B) = P (A) \Rightarrow A \cap B = A \Rightarrow a ⊏ B$

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Similar questions

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

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

In each of the questions choose the correct answer.
If A and B are events such that $P (\frac{A}{B}) = P \frac{B}{A},$ then
(a) $A \subset B b u t A \neq B$

(b) A = B

(d) P(A) = P(B)

A and B are two events such that $P (A) \neq 0$ . Find $P (\frac{B}{A})$ if
$A \cap B = ϕ$

If A and B are two events such that P (A) ≠ 0 and P(B|A) = 1, then.

(A) A ⊂ B

(B) B ⊂ A

(D) A = Φ

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If A and B are two events such that P (A) ≠0 and P(BA)=t, then (a) A⊏B (b) B⊏A (c) B=ϕ (d) A=ϕ

Given, P(A)≠0andP(BA)=1⇒P(BA)=P(A∩B)P(A)=1⇒P(A∩B)=P(A)⇒A∩B=A⇒a⊏B

If A and B are two events such that P (A) $\neq 0$ and

$P (\frac{B}{A}) = t,$ then

(a) $A ⊏ B$ (b) $B ⊏ A$
(c) $B = ϕ$ (d) $A = ϕ$

Given, $P (A) \neq 0 a n d P (\frac{B}{A}) = 1 \Rightarrow P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)} = 1 \Rightarrow P (A \cap B) = P (A) \Rightarrow A \cap B = A \Rightarrow a ⊏ B$