Assertion - Two events A and B are such that PA - 1-3 and PB - 2-3 then PA- B -2-3Reason - If PB - PA- then PA- B - PB

We know that, P(B) = P(A), then, P(B) ≤ P(A∪ B) ≤ 1 and 0 ≤ P(A ∩ B) ≤ P(A) Now P(B)=2/3, P(A) =1/3 ∴ P(B) gt; P(A) ⇒ P(A∪ B)≥ P(B) ⇒ P(A∪ B) ≥2/3 So, assert ...

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Byju's Answer

Standard VI

Mathematics

Experimental Probability

Assertion : T...

Question

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

Both assertion and reason are true but reason is not the correct 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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Both assertion and reason are true and reason is the correct explanation of assertion.

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Solution

The correct option is D Both assertion and reason are true and reason is the correct explanation of assertion.
We know that, P(B) = P(A), then,
$P (B) \leq P (A \cup B) \leq 1$ and $0 \leq P (A \cap B) \leq P (A)$
Now $P (B) = \frac{2}{3}, P (A) = \frac{1}{3}$
$∴ P (B) > P (A) \Rightarrow P (A \cup B) \geq P (B)$
$\Rightarrow P (A \cup B) \geq \frac{2}{3}$
So, assertion and reason both are true and reason is the correct explanation of assertion.

Suggest Corrections

Similar questions

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
(i) P (A) = 1/3, P (B) = 1/4 and P (A ∪ B) = 5/12, find P (A/B) and P (B/A).
(ii) P (A) =

\frac{6}{11},

P (B) =

\frac{5}{11}

and P (A ∪ B) =

\frac{7}{11},

find P (A ∩ B), P (A/B), P (B/A).
(iii) P (A) =

\frac{7}{13},

P (B) =

\frac{9}{13}

and P (A ∩ B) =

\frac{4}{13},

find

P (A / B) .

Q. If A and B are two events such that

(i) P (A) = \frac{1}{3}, P (B) = \frac{1}{4} and P (A \cup B) = \frac{5}{12}, then find P (A | B) and P (B | A) . (ii) P (A) = \frac{6}{11}, P (B) = \frac{5}{11} and P (A \cup B) = \frac{7}{11}, then find P (A \cap B), P (A | B) and P (B | A) . (iii) P (A) = \frac{7}{13}, P (B) = \frac{9}{13} and P (A \cap B) = \frac{4}{13}, then find P (A | B) . (iv) P (A) = \frac{1}{2}, P (B) = \frac{1}{3} and P (A \cap B) = \frac{1}{4}, then find P (A | B), P (B | A), P (A | B) and P (A | B) .

[NCERT EXEMPLAR]

Q. If A and B are two events, then P (

A

∩ B) =
(a) P

(A)

(B)

(b) 1 − P (A) − P (B)
(c) P (A) + P (B) − P (A ∩ B)
(d) P (B) − P (A ∩ B)

Q. Assertion :If A & B are two events such that

P (A) = \frac{2}{5}

P (B) = \frac{3}{4}

then

\frac{1}{20} \leq P (A \cap B) \leq \frac{2}{5}

. Reason:

P (A \cup B) \leq max {P (A), P (B)}

P (A \cap B) \geq min {P (A), P (B)}

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Assertion : Two events A and B are such that P(A)=13 and P(B)=23 then P(A∪B)≥23 Reason : If P(B)>P(A), then P(A∪B)≥P(B)

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