# RS Aggarwal Class 12 Chapter 32 Solutions (Binomial Distribution)

RS Aggarwal Solutions for Class 12 Chapter 32 Binomial Distribution is prepared to provide you assistance while preparing for CBSE Class 12 Board exams. It is a very easy chapter in RS Aggarwal Solutions if you understand and learn the formula of the binomial distribution. The topics discussed in the exercise solutions of this chapter are- introduction to the binomial distribution, Bernoulli Trials to which the concept of binomial distributions is sourced from, the formula for the binomial expansion in keeping in mind the assumptions made for the application of the formula.

There are a total of 5 questions in 1 exercise in the RS Aggarwal Class 12 Maths Solutions for Chapter 32 – Binomial Distribution. These questions are of diverse variety ranging from short answer type to long subjective answers where you are required to analyze the situation. The exercise-questions are very important from the Board and other competitive examination perspectives as well.

The subject matter experts at Instasolv provide you with a step by step answer to each and every question present in this chapter. The reasons for each step are also mentioned besides the algorithm to solve the given problems in the exercise. You will become proficient in time management as well as accuracy rate if you follow the RS Aggarwal Solutions seriously.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 32 – Binomial Distribution

**Introduction**

The prefix ‘bi’ means two or twice. A binomial distribution can be understood as the probability of a series with two and only two consequences. It is a type of distribution that only has two outcomes which are: ‘success’ and ‘failure’. It is applicable to discrete random variables only. The concept of Binomial distribution can be sourced to Bernoulli’s trial.

**Bernoulli Trials**

The binomial distribution is the total sum of a number of discrete independents and identically scattered Bernoulli Trials. In this experiment, the trials are to be random and could have only two outcomes whether it can be success or failure. The flipping of a coin is the best example of Bernoulli trials; each trial can only produce one of the two values- heads or tails. Each time we flip the coin there is a 50% probability of the outcome.

**Binomial Distribution**

The binomial distribution is a common way to test the distribution and it is frequently used in statistics. There are two most important variables in the binomial formula such as:

- ‘n’ represents the total number of times the experiment was conducted
- ‘p’ represents the possibility of one specific outcome

It is also being used in social science statistics as elementary units for the models of variables with two outcomes. We can take the examples of election polls; whether the party ‘A’ will win or the party ‘B’ will win in the upcoming election. Whether by executing a certain policy the government will get the anticipated results within a specific period or not.

There are three different criteria of binomial distributions described below which the binomial distributions need to fulfil.

- The number of trials of the experiment must be fixed. As we can only figure out the probable chance of occurrence of success in a trail we should have a finite number of trials.
- Every trial is independent. None of our trials should affect the possibility of the next trial.
- The probability always stays the same and equal. The probability of success may be equal for more than one trial.

**Binomial Distribution – Formula:**

**b(x,n,p)= nCx*P ^{x*}(1-P)^{n-x} **for x=0,1,2,…..n.

where: –b is the binomial probability.

x is the total number of successes.

p is the chance of success in an individual experiment.

n is the number of trials

**Important Highlight about the formula:**

In the formula:

- n>0 ∴ p, q≥0
- ∑b(x,n,p) = b(1) + b(2) + … + b(n) = 1
- The value of ‘n’ and ‘p’ must be known for applying the above formula.

**Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 32 Binomial Distribution**

- The first and only exercise comprises 5 analytical questions which will help you in rigorous practice and comprehensive revision.
- The questions and answers are in accordance with the latest CBSE exam pattern and guidelines to approach a question of these topics.
- The exercise question solutions have covered each question in order to make sure you don’t have to hop from one source to another.

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