Important Formulas on Binomial Distribution

The table below represents the important formulas of Binomial distribution.

Where,

• n is number of trials
• p is probability of success
• q is probability of failure
• μ is mean or expected value
• Var(X) is variance
• σ is standard deviation

Binomial Distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, where each trial has only two possible outcomes: success or failure.

Imagine you’re flipping a coin, but not just once – you’re flipping it many times. Each time, you’re either getting heads or tails. The binomial distribution helps us figure out the chances of getting a certain number of heads (or tails) after flipping the coin a bunch of times.

Here are a few examples of situations that can be modelled using the binomial distribution:

• Suppose you flip a fair coin 10 times. Each flip is an independent trial, and there are only two possible outcomes: heads or tails.
• In a clinical trial, patients are often given a treatment or a placebo. The outcome for each patient might be success (the treatment works) or failure (the treatment doesn’t work).
• A factory produces a large number of items, and each item may be defective or non-defective. Inspectors randomly select a sample of items and check them for defects.
• In an election where voters can choose between two candidates, each voter’s decision can be seen as a trial with two possible outcomes: voting for Candidate A or voting for Candidate B.