Definition
Independent events
Independent events are events where learning one result does not change the chance of the other.
Continue from this idea into connected AXIO math.
One result gives no chance-changing clue about the other.
Boundary: Events can be independent even when they happen in the same experiment; events that look separate can still be dependent.
What it means
Think of two tosses of a fair coin. The first toss can be heads or tails, but that result does not make heads more or less likely on the second toss. Independence is a relationship between probabilities, not simply a claim that two events sound unrelated.
Remember it
One result gives no chance-changing clue about the other.
Example
A fair coin is tossed twice. The chance of heads on each toss is 1/2. The chance of heads both times is 1/4, and 1/4 = (1/2) × (1/2), so the two heads-events are independent.
Watch for
Events can be independent even when they happen in the same experiment; events that look separate can still be dependent.
Common mix-up
Independent does not mean mutually exclusive. Two non-impossible mutually exclusive events cannot both happen, so they are not independent.
Exact meaning
Events A and B are independent when the chance that both happen equals P(A) × P(B). After either result is known, the probability assigned to the other stays the same.