Binomial Distribution Examples
Let’s say we toss a coin twice, and getting head is a success we have to calculate the probability of success and failure then, in this case, we will calculate the probability distribution as follows:
In each trial getting a head that is a success, its probability is given as p = 1/2
n = 2 as we throw a coin twice
r = 0 for no success, r = 1 for getting head once and r = 2 for getting head twice
Probability of failure q = 1 – p = 1 – 1/2 = 1/2.
P(Getting 1 head) = P(X = 1) = ncrprqn-r = 2c1(1/2)1(1/2)1 = 2 ⨯ 1/2 ⨯ 1/2 = 1/2
P(Getting 2 heads) = P(X = 2) = 2c2(1/2)2(1/2)0 = 1/4
P(Getting 0 heads) = P(X = 0) = 2c0(1/2)0(1/2)2 = 1/4
Random Variable (X = r) |
P(X = r) |
---|---|
X = 0 (Getting 0 Head) |
1/4 |
X = 1 (Getting 1 Head) |
1/2 |
X = 2 (Getting 2 Head) |
1/4 |
As of now, we know that Binomial Distribution is calculated for the Random Variables obtained in Bernoulli Trials. Hence, we should understand these terms.
Binomial Distribution in Probability
Binomial Distribution in Probability gives information about two types of possible outcomes i.e. Success or Failure. Binomial Probability Distribution is a discrete probability distribution used for the events that give results in ‘Yes or No’ or ‘Success or Failure’.
Binomial distribution is calculated by multiplying the probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials.
In this article, we will learn about binomial probability distributions, binomial distribution formulas, binomial distribution meaning, and properties of a binomial distribution.
Table of Content
- What is Binomial Distribution in Probability?
- Binomial Distribution Definition
- Binomial Distribution Meaning
- Binomial Distribution Formula
- Binomial Distribution Calculation
- Binomial Distribution Examples
- Bernoulli Trials in Binomial Distribution
- Binomial Random Variable
- Binomial Distribution Table
- Binomial Distribution Graph
- Binomial Distribution in Statistics
- Measure of Central Tendency for Binomial Distribution
- Binomial Distribution Mean
- Binomial Distribution Variance
- Binomial Distribution Standard Deviation
- Binomial Distribution Properties
- Binomial Distribution Applications
- Negative Binomial Distribution
- Negative Binomial Distribution Formula
- Binomial Distribution vs Normal Distribution
- Binomial Distribution in Probability – Solved Examples
- Practice Problems on Binomial Distribution in Probability
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