Class 12 RS Aggarwal Chapter-31 Probability Distribution Solutions - Free PDF Download
FAQs on RS Aggarwal Class 12 Solutions Chapter-31 Probability Distribution
1. How do RS Aggarwal Class 12 Solutions for Chapter 31 help in mastering Probability Distribution?
RS Aggarwal solutions for Probability Distribution offer a comprehensive set of problems that go beyond the basic NCERT exercises. They help you master the topic by providing practice on a wide variety of question types, including complex word problems. This ensures you can apply concepts like random variables, mean, and variance to different scenarios, which is crucial for the CBSE board exams.
2. Are the problem-solving methods in RS Aggarwal solutions for Probability Distribution aligned with the 2025-26 CBSE board exam pattern?
Yes, the step-by-step methods provided in the solutions are fully aligned with the 2025-26 CBSE marking scheme. The answers are structured to show the clear application of formulas and logical steps, from defining the random variable to calculating the final answer. This helps students understand how to present their answers in the exam to secure full marks.
3. What is the correct first step when solving a problem on probability distribution from RS Aggarwal Class 12?
The most crucial first step is to clearly define the random variable (X). The random variable represents the numerical outcome of a random phenomenon in the experiment. For example, if you toss two coins, the random variable X could be 'the number of heads'. Correctly defining X is fundamental to constructing the probability distribution table accurately.
4. What is the step-by-step method to calculate the mean of a probability distribution as shown in the solutions?
The mean, or Expected Value E(X), is calculated using a clear, step-by-step process:
- First, construct the probability distribution table listing all possible values of the random variable (xᵢ) and their corresponding probabilities (pᵢ).
- Next, for each value of X, multiply the value by its probability to get the product xᵢpᵢ.
- Finally, sum all these products. The formula is E(X) = Σxᵢpᵢ. This sum gives you the mean of the distribution.
5. How do you calculate the variance for a random variable in a Class 12 probability problem?
The variance, denoted as Var(X) or σ², measures the spread of the distribution. The solutions guide you to calculate it using the formula: Var(X) = E(X²) - [E(X)]². The steps are:
- First, calculate the mean, E(X).
- Second, calculate E(X²) by summing the products of the square of each random variable value and its probability (Σxᵢ²pᵢ).
- Finally, substitute these values into the formula to find the variance.
6. Why is it essential to check if the sum of all probabilities (ΣP(X)) equals 1 in a probability distribution problem?
Checking that ΣP(X) = 1 is a critical verification step. It confirms that your probability distribution is valid and complete. If the sum is not equal to 1, it indicates an error in your calculation of individual probabilities or that you have missed one of the possible outcomes of the random variable. This check helps prevent carrying an initial error through to the final calculations for mean and variance.
7. How can a student identify when to apply the binomial distribution formula for a problem in RS Aggarwal?
You should apply the binomial distribution formula when the problem describes an experiment that satisfies the following conditions:
- There is a fixed number of trials (n).
- Each trial is independent of the others.
- Each trial has only two possible outcomes: 'success' or 'failure'.
- The probability of success (p) remains constant for each trial.
If these four conditions are met, the problem is a case of binomial distribution.
8. What is a common mistake students make when finding the variance of a probability distribution, and how do the solutions help prevent it?
A very common mistake is confusing E(X²) with [E(X)]². Students often calculate the mean E(X) and simply square it, which is incorrect. The solutions prevent this by clearly showing the two separate calculations: first finding E(X) (the mean), and then separately calculating E(X²) by multiplying each squared x-value with its probability before using the variance formula. This methodical approach highlights the difference and ensures accuracy.
