Independent Events Calculator
Calculate the joint probability of two independent events occurring together by multiplying their individual probabilities.
P(A and B)
0.150000
P(A and B) vs P(A)
Formula
## 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).
Esempio Risolto
A coin has P(heads) = 0.5 and a die has P(six) = 0.3 (loaded). What is the probability of both?
- 01P(A and B) = P(A) * P(B)
- 02P(heads and six) = 0.5 * 0.3 = 0.15
- 03P(heads or six) = 0.5 + 0.3 - 0.15 = 0.65
- 04P(neither) = (1 - 0.5) * (1 - 0.3) = 0.5 * 0.7 = 0.35
Domande Frequenti
How do I know if two events are independent?
Events are independent if P(A|B) = P(A), or equivalently P(A and B) = P(A) * P(B). In experiments, events from separate random processes are typically independent.
What if events are not independent?
For dependent events, use the general multiplication rule: P(A and B) = P(A) * P(B|A), which requires the conditional probability.
Does independent mean mutually exclusive?
No. Mutually exclusive events cannot occur together (P(A and B) = 0). Independent events can occur together; their joint probability is P(A)*P(B) > 0 (assuming both have nonzero probability).
Impara