If P(AUB) = P(ANB) for any two events A and B,
then
P(A)=P(B)
P(A) <PB)
P(A)> PB)
None of these
Answers
Given : P(AUB) = P(A∩B) for any two events A and B
To Find : Correct option
P(A)=P(B)
P(A) <PB)
P(A)> PB)
None of these
Solution:
P(AUB) = P(A) + P(B) - P(A∩B)
=> P(A) + P(B) = P(AUB) + P(A∩B)
P(AUB) = P(A∩B)
=> P(A) + P(B) = P(AUB) + P(AUB)
as P(AUB) ≥ P(A) , P(B)
This is only possible when
P(AUB) = P(A) and P(AUB) = P(B)
Hence
P(A) = P(B)
Correct option is P(A) = P(B)
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SOLUTION
TO CHOOSE THE CORRECT OPTION
If P(AUB) = P(A∩B) for any two events A and B,
then
P(A) = P(B)
P(A) < P(B)
P(A) > P(B)
None of these
EVALUATION
Here it is given that
P(AUB) = P(A∩B)
We are aware of the formula on probability that
P(AUB) = P(A) + P(B) - P(A∩B)
⟹ P(A∩B) = P(A) + P(B) - P(A∩B)
⟹ P(A∩B) - P(A) = P(B) - P(A∩B) - - - - - (1)
Again we know that
P(A∩B) ≤ P(A) and P(A∩B) ≤ P(B)
So the Expression 1 is possible only if
P(A∩B) = P(A) = P(B)
FINAL ANSWER
Hence the correct option is
P(A) = P(B)
━━━━━━━━━━━━━━━━
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