Binomial Distribution Calculator

Number of Trials (n):

Probability of Success (p):

Number of Successes (k):

Results

Understanding Binomial Distribution

What is Binomial Distribution?

The binomial distribution models the number of successes in a fixed number of independent trials, where each trial has the same probability of success. Key characteristics include:

Fixed number of trials (n)
Independent trials
Constant probability of success (p)
Only two possible outcomes per trial (success/failure)

Key Formulas

Probability Mass Function:

P(X = k) = C(n,k) * p^k * (1-p)^(n-k)

Mean (Expected Value):

μ = np

Variance:

σ² = np(1-p)

Standard Deviation:

σ = √(np(1-p))

Properties

Shape

Symmetric when p = 0.5
Right-skewed when p < 0.5
Left-skewed when p > 0.5

Characteristics

Discrete probability distribution
Sum of probabilities equals 1
Non-negative probabilities

Applications

Quality Control

Testing defective items in manufacturing

Medicine

Clinical trials and drug testing

Finance

Risk assessment and insurance