For two given events A and B, P(A⋂B) is :

Engineering

Mathematics

Conditional Probability

Question

not less than P(A) + P(B) – 1

not greater than P(A) + P(B)

equal to P(A) + P(B) – P(AUB)

equal to P(A) + P(B) + P(A⋂B)

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$∴ P(AUB) = P(A) + P(B) - P(A⋂B)$
on rearranging we get
$P(A⋂B) = P(A) + P(B) - P(AUB)$ which is option C
Also ∵ 0 ≤ P(AUB) ≤ 1

$\Rightarrow P(A) + P(B) - 1 \leq P(A⋂B) \leq P(A) + P(B)$
Hence B and C are also correct
Now if P(A⋂B) = P(A) + P(B) + P(A⋂B)

$\Rightarrow P(A) + P(B) = 0$

which is not necessary for the events A and B
Hence the correct options are A,B and C

Please subscribe our Youtube channel to unlock this solution.