(B) Given that $P(A) + P(B) = 2 P(A \cap B)$.We know the addition theorem of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the g

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(B) Given that $P(A) + P(B) = 2 P(A \cap B)$.We know the addition theorem of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the given condition into the formula:$P(A \cup B) = 2 P(A \cap B) - P(A \cap B) = P(A \cap B)$.Since $P(A \cap B) \leq P(A) \leq P(A \cup B)$ and $P(A \cap B) \leq P(B) \leq P(A \cup B)$, the equality $P(A \cup B) = P(A \cap B)$ implies that $P(A) = P(B) = P(A \cap B) = P(A \cup B)$.Thus, $P(A) = P(B)$.

Class 11 Mathematics Probability Odds in favor and odds against, Addition theorem on probability

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If $A$ and $B$ are two events in a random experiment such that $P(A) + P(B) = 2 P(A \cap B)$, then:

TS EAMCET 2023 All TS EAMCET

A
$P(A) + P(B) = 1$
B
$P(A) = P(B)$
C
$P(A) + P(B) > 1$
D
$P(A) = 0, P(B) = 1$

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Odds in favor and odds against, Addition theorem on probability

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