You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Logarithms

For any two e...

Question

For any two events A and B, which one of the following holds?

P (A \cap B) \leq P (A) \leq P (A \cup B) \leq P (A) + P (B)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

P (A \cup B) \leq P (A) \leq P (A \cap B) \leq P (A) + P (B)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

P (A \cup B) \leq P (B) \leq P (A \cap B) \leq P (A) + P (B)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

P (A \cap B) \leq P (B) \leq P (A) + P (B) \leq P (A \cup B)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $P (A \cap B) \leq P (A) \leq P (A \cup B) \leq P (A) + P (B)$
By seeing the above figure, we can see the value of each element and intersections.
$∴ P (A \cap B) \leq P (A) \leq P (A \cup B) \leq P (A) + P (B)$

Suggest Corrections

Similar questions

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

(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 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. Assertion :If

P (A / B) = P (B / A)

. A, B are two non mutually exclusive events then

P (A) = P (B)

. Reason: For non mutually exclusive events

(A \cap B) \neq ϕ

and

P (A / B) = \frac{P (A \cap B)}{P (B)}

P (B / A) = \frac{P (A \cap B)}{P (A)}

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

Join BYJU'S Learning Program

For any two events A and B, which one of the following holds?

The correct option is A P(A∩B)≤P(A)≤P(A∪B)≤P(A)+P(B)By seeing the above figure, we can see the value of each element and intersections.∴ P(A∩B) ≤P(A) ≤P(A∪B)≤P(A)+P(B)

The correct option is A $P (A \cap B) \leq P (A) \leq P (A \cup B) \leq P (A) + P (B)$
By seeing the above figure, we can see the value of each element and intersections.
$∴ P (A \cap B) \leq P (A) \leq P (A \cup B) \leq P (A) + P (B)$