RD Sharma Class 12 Chapter 33 Solutions (Binomial Distribution)

RD Sharma Class 12 Maths Solutions Chapter 33 Binomial Distribution teaches you the concept of Binomial Distribution or a particular type of probability distribution in detail. Did you know Binomial Distribution was first introduced by James Bernoulli in 1700? The topics you’re going to learn in this chapter are Bernoulli trials, Binomial Distribution, Mean and Variance of Binomial Distribution, etc. This chapter is small as compared to the other topics of RD Sharma Class 12 Maths Solutions. However, it is a very important one as you can expect questions on Binomial Distribution in your exams.

This chapter comprises two exercises and 70 questions in total. You’ll be getting help around questions based on finding the probability of the event’s occurrence for a given number of times in independent trials’ series, finding the probability distribution, calculating the number of trials when you have the probability of event’s occurrence, determining the frequency of a number of successes, etc.

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Some Topics Discussed in RD Sharma Class 12 Maths Solutions Chapter 33

Bernoulli Trials 

In your everyday life, you might have seen many dichotomous experiments. Dichotomous experiments are the ones that produce one of the two outcomes in a trial. For example, you may see on tossing a coin you either get ahead or you get a tail. This is an example of a dichotomous experiment. Also as you purchase a manufactured item, you are lucky to get it non-defective or unlucky if it comes out defective. These experiments produce two outcomes out of which one should be a success and the other a failure. Repeating such experiments under identical conditions, the outcome of one trial will not be dependent on the outcome of the other trial. In every trial, the probability of failure or the probability of success will remain constant. And the trials where there are only two outcomes, i.e. a success or a failure are known as Bernoulli  Trials. Any experiment will be a Bernoulli trial if it meets the following criteria:

  1. The number is finite
  2. All the experiments should be independent of each other
  3. Every trial will have two outcomes: a failure and a success
  4. The probability of the two outcomes i.e. a failure and a success will remain the same.

Binomial Distribution 

Consider a random variable X that takes values such as 0, 1, 2, …, n. X will follow binomial distribution if and only if its probability distribution function is

Note – Consider an experiment with n trials. Consider the same experiment to be repeated at least N times, then the frequencies of successes 0,1, 2, 3, …, n is

N.P(X=0), N.P(X=1), N.P(X=2), …, N.P(X=n).

Discussion of exercises in RD Sharma Class 12 Maths Solutions Chapter 33 Binomial Distribution

  1. Exercise 33.1 discusses questions on calculating the probability of event’s occurrence for a specific and given number of times in all the independent trials, finding the probability distribution, calculating the frequency of the number of successes in trials, calculating the trials when you know the probability of occurrence of an event, etc. This exercise comprises 49 questions in total.
  2. Exercise 33.2 emphasizes on questions like finding the mean and variance of the binomial distribution, etc. The exercise comprises 21 questions. You will answer questions like proving the mean of a binomial distribution will be greater than its variance, given the values of variance and mean of a binomial distribution you will determine the distribution, etc.

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  6. Solutions to these questions are arranged in the same order as they have arranged in RD Sharma Solutions Chapter 33 Binomial Distribution.