Answer:
Two events, A and B, are independent if the occurrence of one event does not affect the probability of the other event occurring. Mathematically, this can be expressed as:
\[ P(A \cap B) = P(A) \cdot P(B) \]
Where \( P(A \cap B) \) is the probability that both events A and B occur, \( P(A) \) is the probability of event A occurring, and \( P(B) \) is the probability of event B occurring. If this equation holds true, then events A and B are independent.
Another way to check for independence is to use conditional probabilities. Two events are independent if:
\[ P(A|B) = P(A) \]
or equivalently,
\[ P(B|A) = P(B) \]
Where \( P(A|B) \) is the probability of event A occurring given that event B has occurred, and \( P(B|A) \) is the probability of event B occurring given that event A has occurred. If either of these conditions is satisfied, then A and B are independent.
