Independent Events Calculator Formula
Understand the math behind the independent events calculator. Each variable explained with a worked example.
Formulas Used
P(A and B)
p_both = p_a * p_bP(A or B)
p_either = p_a + p_b - p_a * p_bP(Neither)
p_neither = (1 - p_a) * (1 - p_b)Variables
| Variable | Description | Default |
|---|---|---|
p_a | P(A) | 0.5 |
p_b | P(B) | 0.3 |
How It Works
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).
Worked Example
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
Frequently Asked Questions
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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Open Independent Events Calculator