# Thread: Calculating probability of an event

1. ## Calculating probability of an event

Find the probability of the following event :

$P(A \cap B | A \cup B )$

Attempt to solution :

$P(A \cap B | A \cup B )= \frac{P(A \cap B \cap A \cup B)}{P(A \cup B)}= \frac{P(A)}{P(A \cup B)}$

$(A \cap B) \subset (A \cup B )$ the intersection is the smaller set $A \cap B$
$P(A \cap B | A \cup B )= \frac{P(A \cap B )}{P(A \cup B)}$