Suppose A and B are two events such that P(A) | vedclass

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(A) We know that for any two events $A$ and $B$,the probability of their union is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Given $P(A) = 0.9

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Always true

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(A) We know that for any two events $A$ and $B$,the probability of their union is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Given $P(A) = 0.9$ and $P(B) = 0.8$,we have $P(A \cup B) = 1.7 - P(A \cap B)$.Since $P(A \cap B) \geq 0.7$,the maximum value of $P(A \cap B)$ is $0.9$ (because $P(A \cap B) \leq P(A)$ and $P(A \cap B) \leq P(B)$).Also,$P(A \cup B) \leq 1$ must hold for any probability space.Substituting the minimum value of $P(A \cap B) = 0.7$,we get $P(A \cup B) = 1.7 - 0.7 = 1.0$.Since $P(A \cup B)$ can be at most $1$,and the condition $P(A \cap B) \geq 0.7$ allows for valid probability values,this case is always true.

Suppose $A$ and $B$ are two events such that $P(A) = 0.9$,$P(B) = 0.8$,and $P(A \cap B) \geq 0.7$. Then,we can conclude that such a case is . . . . . .

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