Binomial Distribution

What is Binomial Distribution and its Properties?

Binomial distribution is probability distribution that calculates the probability of x success by using number of trials, success probability and failure probability.

What are the 4 Factors of Binomial Distribution?

The 4 factors of binomial distribution are: number of trials, number of successes, probability of success and probability of failure.

What is the Main Formula of Binomial Distribution?

The main formula of Binomial distribution is given by:

P (X = x) = ⁿC_x p^x q^n-x

How to Find q in Binomial Distribution?

To find q i.e., probability of failure in binomial distribution we calculate 1 – p where, p is the probability of success.

What is p in Binomial Distribution?

p in Binomial distribution is the probability of success.

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.