Binomial distribution

1. A binomial distribution is a probability of SUCCESS or FAILURE in an experiment that is repeated many times.
2. It is call Binominal because we will have only two outcomes.
3. Binomial is a discrete because the values are fixed

For Eg: I want to roll a dice and expecting six, I will either get six (SUCCESS) or any other values(FAILURE),here I might get the value from 1 to 6 , but not 1.1,1.23 etc..

In short anything you think about SUCCESS or FAILURE like if I propose my love to my dream girl, Will she accepts or not(SUCCESS or FAILURE )

We will understand more with below examples between SUCCESS and FAILURE.

What is the probability of getting heads when I toss a coin.

If we are expecting a heads then heads will be SUCCESS and tails will be FAILURE.Below is the probability of SUCCESS and FAILURE.

We have two formulas to calculate the Binomial Distribution.

Where:

b = binomial probability

x = total number of “successes” (pass or fail, heads or tails etc.)

P = probability of a success on an individual trial

Q = probability of a failure (means 1-P)

n = number of trials

We need to understand how to calculate combinations and factorial,click here to know

We will take one example and solve the Binomial problem.

A coin is tossed 10 times. What is the probability of getting exactly 4 heads?

From our question

n=10

x=4

p=0.5

q=1-p=0.5

We will use Formula 2 to calculate

So there will be 20.5% probability of getting 4 heads when I toss 10 times.