For any two possible events A and B the expression P((A/A ∪ B)) is always equal to

Question

For any two possible events A and B the expression P((A/A ∪ B)) is always equal to (A) (P(A ∪ B)-P(B)/P(A ∪ B)) (B) (P(A ∪ B)-P(A)/P(A ∪ B)) (C) ( P ( A ∪ B )- P ( B )+ P ( A ∩ B )/ P ( A ∪ B )) (D) (P(A ∪ B)+P(B)-P(A ∩ B)/P(A ∪ B))

Tardigrade Admin · Accepted Answer

(P(A ∩(A ∪ B))/P(A ∪ B))=(P(A)/P(A ∪ B))=(P(A ∪ B)-P(B)+P(A ∩ B)/P(A ∪ B)).

Q. For any two possible events $A$ and $B$ the expression $P (\frac{A}{A \cup B})$ is always equal to

$\frac{P ( A \cup B ) - P ( B )}{P ( A \cup B )}$

$\frac{P ( A \cup B ) - P ( A )}{P ( A \cup B )}$

$\frac{P ( A \cup B ) - P ( B ) + P ( A \cap B )}{P ( A \cup B )}$

$\frac{P ( A \cup B ) + P ( B ) - P ( A \cap B )}{P ( A \cup B )}$

$\frac{P ( A \cap ( A \cup B ))}{P ( A \cup B )} = \frac{P ( A )}{P ( A \cup B )} = \frac{P ( A \cup B ) - P ( B ) + P ( A \cap B )}{P ( A \cup B )}$ .

Q. For any two possible events A and B the expression P(A∪BA​) is always equal to

P(A∪B)P(A∪B)−P(B)​

P(A∪B)P(A∪B)−P(A)​

P(A∪B)P(A∪B)−P(B)+P(A∩B)​

P(A∪B)P(A∪B)+P(B)−P(A∩B)​