ProbabilityHard
Question
For any two events A and B in a sample space
Options
A.P
P(B) ≠ 0 is always true
P(B) ≠ 0 is always trueB.P(A ∩ 
) = P(A) - P(A ∩ B) does not hold
) = P(A) - P(A ∩ B) does not holdC.P(A ∪ B) = 1- P(
)P(
) if A and B are independent
)P() if A and B are independentD.P(A ∪ B) = 1- P()P() if A and B are disjoint
)P() if A and B are disjointSolution
We know that,
P
Since, P(A ∪ B) < 1
⇒ - P(A ∪ B) > - 1
⇒ P(A) + P(B) - P(A ∪ B) > P(A) + P(B) -1
⇒
⇒ P
Option (a) is correct.
The choice (b) holds only for disjoint ie, P(A ∩ B) = 0
Finally, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= P(A) + P(B) - P(A).P(B)
If A,B are independent
= 1 - {1 - P(A)} {1 - P(B)}
= 1 - P(
).P(
)
∴ Option (c) is correct, but option (d) is not correct.
P
Since, P(A ∪ B) < 1
⇒ - P(A ∪ B) > - 1
⇒ P(A) + P(B) - P(A ∪ B) > P(A) + P(B) -1
⇒
⇒ P
Option (a) is correct.
The choice (b) holds only for disjoint ie, P(A ∩ B) = 0
Finally, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= P(A) + P(B) - P(A).P(B)
If A,B are independent
= 1 - {1 - P(A)} {1 - P(B)}
= 1 - P(
).P()∴ Option (c) is correct, but option (d) is not correct.
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