Independent Events Calculator — Formule
## How to Calculate Joint Probability of Independent Events
### Formula
**P(A and B) = P(A) * P(B)**
Two events are independent if the occurrence of one does not affect the probability of the other. For independent events, the joint probability is simply the product of the individual probabilities. This extends to any number of events: P(A and B and C) = P(A) * P(B) * P(C).
### Formula
**P(A and B) = P(A) * P(B)**
Two events are independent if the occurrence of one does not affect the probability of the other. For independent events, the joint probability is simply the product of the individual probabilities. This extends to any number of events: P(A and B and C) = P(A) * P(B) * P(C).
Exemple Résolu
A coin has P(heads) = 0.5 and a die has P(six) = 0.3 (loaded). What is the probability of both?
- P(A and B) = P(A) * P(B)
- P(heads and six) = 0.5 * 0.3 = 0.15
- P(heads or six) = 0.5 + 0.3 - 0.15 = 0.65
- P(neither) = (1 - 0.5) * (1 - 0.3) = 0.5 * 0.7 = 0.35