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Berechnen Sie joint probability of independent events. Multiply individual probabilities for the combined result.
P(A and B)
0.150000
P(A and B) vs P(A)
Formel
## 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).
Lösungsbeispiel
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
Häufig Gestellte Fragen
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).
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