Independence Is a Probability Relationship

Events A and B are independent when learning that one occurred does not change the probability of the other.

Equivalent checks include

P(A ∩ B) = P(A)P(B)

and, when the relevant denominators are nonzero,

P(A|B) = P(A).

Independence is different from mutual exclusivity. If two positive-probability events are mutually exclusive, they cannot occur together, so their intersection probability is zero rather than the positive product P(A)P(B).

Use exact fractions when testing independence so two rounded decimals do not appear equal by accident.