Probability Distributions
Binomial Distribution:
The problems relating to tossing of coins or throwing of dice or drawing cards from a pack of cards with replacement lead to binomial probability distribution.
Only two possibilities are in Binomial distribution.
p = Probability of success
q = Probability of failure = 1 p .. ... .. .. .. Since only two outcomes, success and failure, are possible
n = no. of total attempts
x = no. of successful attempts = 0,1,2,3,.. .. .. ,n
Then probability of success P(x) is given by:\[\large P(x)= C(n,x)p^{x}q^{nx} = \frac{n!}{x!(nx)!}p^{x}q^{nx}\]
Condition for Binomial Distribution:
We get the Binomial distribution under the following experimental conditions.

The number of trials ā nā is finite.

The trials are independent of each other.

The probability of success ā pā is constant for each trial.

Each trial must result in a success or a failure.