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Probabilities
P(X=x)  =  e^{λ} 
λ^{x}
x!

λ≥0, x≥0
Calculator (fill all fields and click 'Calculate'):
Expected (average) number of events:λ =
P(X = x):
P(X ≤ x):
P(X ≥ x):
P(X=x)  =  n!
x!(n  x)!

p^{x}(1p)^{nx} 
n>0, 0≤x≤n, 0≤p≤1
Calculator (fill all fields and click 'Calculate'):
Number of trials:n =
Probability of success in one trial:p =
P(X = x):
P(X ≤ x):
P(X ≥ x):
Mean:
P(X=x)  = 

N>0, M>0, M≤N, 0<n≤N, 0≤x≤M, x≤n
Calculator (fill all fields and click 'Calculate'):
Total population size:N =
Subpopulation size:M =
Sample size:n =
P(X = x):
P(X ≤ x):
P(X ≥ x):
Mean:
P(X=x)  =  p(1p)^{x1} 
x>0, 0<p<1
Calculator (fill all fields and click 'Calculate'):
Probability of success in one trial:p =
P(X = x):
P(X ≤ x):
P(X ≥ x):
Mean:
P(X=x)  =  (  x1
k1

)  (1p)^{xk} p^{k} 
P(k, r)  =  (  k+r1
k1

)  (1p)^{r} p^{k} 
x>0, k>0, x≥k, r≥0, 0<p<1; x = k + r
Calculator (fill all fields and click 'Calculate'):
Probability of success in one trial:p =
Number of successes:k =
P(X = x):
P(X ≤ x):
P(X ≥ x):
Mean:
Probabilities Calculator is a free online tool for calculations of probabilities of events following one of the most common discrete probability distributions:
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