Independent events
Two events are independent when the occurrence of one does not change the probability of the other, so P(A and B) = P(A) × P(B). Independence underlies the binomial distribution and is testable through contingency-table analysis.
FrameworkProbability theory
See it move
A customer opens a marketing email 40% of the time and clicks a website ad 25% of the time. If the two behaviours are independent, learning that one happened changes nothing about the other, so the joint probability multiplies: 0.40 times 0.25, giving a 10% chance both occur. Any departure from that product would signal dependence between the events.
The formula
Variables
- Probability of event A
- Probability of event B
- Joint probability that both A and B occur
Equivalent condition: P(A | B) = P(A). If the joint probability does not equal the product of the marginals, the events are dependent.
Check yourself
An insurer estimates P(flood claim) = 0.05 and P(theft claim) = 0.08 for a randomly chosen policy. Assuming independence, what is the probability that a single policy involves both a flood claim and a theft claim in the same year?