Probability Distributions

Useful For: 
Mechanical, Electrical and Computer, Chemical

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:\[\large P(x)= C(n,x)p^{x}q^{n-x} = \frac{n!}{x!(n-x)!}p^{x}q^{n-x}\]

Condition for Binomial Distribution:

We get the Binomial distribution under the following experimental conditions.

  1. The number of trials ā€˜ nā€™ is finite.

  2. The trials are independent of each other.

  3. The probability of success ā€˜ pā€™ is constant for each trial.

  4. Each trial must result in a success or a failure.