Binomial Probability Calculator
Calculate binomial probabilities and distribution statistics
Quick examples:
Quick examples:
Distribution Visualization
Probability
24.6094%
P(X = 5) = 0.24609375
P(X < 5): 37.6953%
P(X ≤ 5): 62.3047%
P(X > 5): 37.6953%
P(X ≥ 5): 62.3047%
Distribution Statistics
5.0000
Mean (μ)
2.5000
Variance (σ²)
1.5811
Std Dev (σ)
Full Distribution
| k | P(X=k) | % |
|---|---|---|
| 0 | 0.000977 | 0.10% |
| 1 | 0.009766 | 0.98% |
| 2 | 0.043945 | 4.39% |
| 3 | 0.117188 | 11.72% |
| 4 | 0.205078 | 20.51% |
| 5 | 0.246094 | 24.61% |
| 6 | 0.205078 | 20.51% |
| 7 | 0.117188 | 11.72% |
| 8 | 0.043945 | 4.39% |
| 9 | 0.009766 | 0.98% |
| 10 | 0.000977 | 0.10% |
Binomial Distribution
P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
μ = np, σ² = np(1-p)
About Binomial Distribution
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success.
When to Use Binomial Distribution
- Fixed number of trials (n)
- Each trial has only two outcomes (success/failure)
- Trials are independent
- Probability of success (p) is constant
Common Examples
- Coin flips: Getting heads in 10 tosses
- Quality control: Defective items in a batch
- Medical trials: Success rate of a treatment
Parameters
- n: Number of independent trials
- k: Number of successes we're calculating probability for
- p: Probability of success on each trial (between 0 and 1)
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