Assertion :If the independent events $A$ & $B$ are such that $0 < P (A) < 1, 0 < P (B) < 1$ , then $A$ & $B$ can not be mutually exclusive. Reason: Two events $A$ & $B$ can not be mutually exclusive, if $P (A \cap B) \neq 0$ .

Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

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Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion

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Assertion is true but Reason is false

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Assertion is false but Reason is true

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Solution

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
Since $A$ & $B$ are independent
$∴ P (A \cap B) = P (A) P (B) \neq 0$
as $0 < P (A) < 1; 0 < P (B) < 1$
$\Rightarrow$ events $A$ & $B$ can not be mutually exclusive.

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Similar questions

Assertion : In rolling a die, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason : In a sample space two events are mutually exclusive if they do not occur at the same time.

Assertion: In rolling a dice, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason: In a sample space, two events are mutually exclusive if they do not occur at the same time.

Q. Assertion : Two events A and B are such that

P (A) = \frac{1}{3}

and

P (B) = \frac{2}{3}

then

P (A \cup B) \geq \frac{2}{3}

Reason : If

P (B) > P (A)

, then

P (A \cup B) \geq P (B)

Q. Assertion: The probability of a sure event is 1.
Reason: Let E be an event. Then,

0 \leq P (E) \leq 1

.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Assertion: If $a \neq b$ , then $(a, b) \neq (b, a)$ .
Reason: $(4, - 3)$ lies in Quadrant $I V$
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Assertion :If the independent events A & B are such that 0<P(A)<1,0<P(B)<1, then A & B can not be mutually exclusive. Reason: Two events A & B can not be mutually exclusive, if P(A∩B)≠0.

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of AssertionSince A & B are independent∴P(A∩B)=P(A)P(B)≠0as 0<P(A)<1;0<P(B)<1⇒ events A & B can not be mutually exclusive.

Assertion :If the independent events $A$ & $B$ are such that $0 < P (A) < 1, 0 < P (B) < 1$ , then $A$ & $B$ can not be mutually exclusive. Reason: Two events $A$ & $B$ can not be mutually exclusive, if $P (A \cap B) \neq 0$ .

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
Since $A$ & $B$ are independent
$∴ P (A \cap B) = P (A) P (B) \neq 0$
as $0 < P (A) < 1; 0 < P (B) < 1$
$\Rightarrow$ events $A$ & $B$ can not be mutually exclusive.