Essentially, the probability distribution formula refers mainly to two types of probability distributions which include normal or Gaussian probability distribution and binomial probability distribution. It is to remember that a table that assigns a probability to each of the possible outcomes of a random experiment is a probability distribution table. In simpler words, it gives the probability for each value of the random variable.

Probability Distribution Formulas

1. Normal Probability Distribution Formula

It is also known as the Gaussian distribution, and it's referring to the equation or graph that is in bell-shape.

The formula for normal probability distribution as stated

Where,

2. Binomial Probability Distribution Formula

It can be defined as the probability that occurred when the event consists of "n" repeated trials and the outcome of each trial may or may not occur.

The formula for binomial probability as stated below

Where,

Solved examples for probability distribution formulas

Example 1: 

Find the probability of getting 8 tails, if a coin is tossed 10 times.

Solution:

Given,

Number of trails(n) = 10

Number of success(r) = 8( getting 8 tails)

Probability of single trail(p) = 0.5

Thus the probability of getting 8 tails is,

The probability of getting 8 tails = 0.0439

Example 2: 

Find the probability for the normal distribution with population mean 2, standard deviation 3 of random variable 5.

Solution:

Given,

x = 5

Mean = μ = 2

Standard deviation = σ = 3

Normal probability distribution

Conclusion

In a word, formulas for probability distribution are necessary to analyze and interpret all sorts of data in different fields. They let us compute the probability of different outcomes by the binomial or normal distributions. All these formulas help in more plausible decision-making since they are based on statistical principles, thus letting us predict and manage uncertainty much better.

Other Related Sections

NCERT Solutions | Sample Papers | CBSE SYLLABUS| Calculators | Converters | Stories For Kids | Poems for Kids| Learning Concepts | Practice Worksheets | Formulas | Blogs | Parent Resource