Binomial PDF Calculator

Enter 0.5 for a fair coin. Values are probabilities, not percentages.
P(X = k)
0.3125
Binomial Distribution Calculator
P(X ≤ k)
0.5
P(X < k)
0.1875
P(X ≥ k)
0.8125
P(X > k)
0.5
C(n, k)
10
Mean (np)
2.5
Variance (np(1−p))
1.25
Standard deviation
1.118034
Answer as a percentage
31.25 %
Distribution
X ~ B(n = 5, p = 0.5)
Worked out from formula R3954 and 1 other source.

How this is worked out

4 steps
  1. C(5, 2) = 10
  2. P(X = 2) = C(n,k) · p^k · (1−p)^(n−k) = 10 × 0.5^2 × 0.5^3 = 0.3125
  3. Mean = np = 5 × 0.5 = 2.5
  4. Variance = np(1−p) = 1.25, sd = 1.1180339887

Results are general information, not financial, tax, legal, medical or engineering advice.