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Xam Idea Class 12 Maths Chapter 14 Solutions: Probability

Xam Idea 12 Maths Solutions for Chapter 14 ‘Probability’ is a comprehensive guide for the planning of examinations for senior secondary school students. These Xam Idea solutions are completely based on CBSE Class 12 guidelines and exam pattern. They will provide you with thorough descriptions of complicated problems and step-by-step solutions that will help you understand the fundamental definition of probability in a more systematic way. Implementing these questions daily can allow you to update everything that relates to this chapter.

Xam Idea Class 12 Maths Solutions for Probability include a total of 68 questions divided into four segments. These segments are Very Short Answer Type Questions, Short Answers, Long Answer Type Questions (Type I & II) respectively. The questions are based on independent distribution, binomial distribution (B), probability distributions, random variability, mean and variance of the distribution, conditional probability, and Bayes theorem.

Xam Idea Class 12 Maths Solutions by instasolv are established by a qualified team of instructors with considerable expertise, covering the syllabus of the Class 12 board exams. The ability to score high marks in Maths will be simple if you take the appropriate route and make your concepts strong. Our Xam Idea Class 12 Solutions are designed in such a way to accommodate all the question-answers in a significant-structured format.

Important Topics of Xam Idea Class 12 Maths Solutions Chapter 14: Probability

  • All our solutions are designed to help to deal with problems that regularly come up in competitive exams like JEE Mains. Let us begin with some important definitions :
  • Probability implies the likelihood. It is a mathematical concept which deals with the existence of a random event. The value of probability is represented between both zero and one. The possibility has been implemented in Maths to determine whether events are likely to happen.
  • It is the fundamental probability principle that is often found in the probability distribution, where you can discover the likelihood of results with a random variable. To assess the probability of a particular occurrence happening, you will first learn the cumulative amount of potential outcomes.

Probability Equation

 

 

A probability equation is defined as the chance of an occurrence appearing is equivalent to the measure of the total of beneficial results and the total number of outcomes.

Probability equation P(E) = amount of  positive outcomes/Total outcomes

 

Conditional Probability:

 

The possibility of any event A happening while another occurrence B has already happened concerning A is regarded as the conditional probability. It is shown by P(A)

  • As seen in the illustration above, the sample space is supplied by S and there are two occurrences A and B. In a scenario where event B has already existed, our sample space S will significantly reduce to B because now the chances of an event occurring are within B.
  • Because we have to figure out the likelihood and impact of event A, only the section specific to both A and B is adequate to represent the probability of event A, since B has indeed existed. The specific portion of events is represented by the intersection of occurrences A and B i.e. A ∩ B.
  • The principle of conditional probability situations illustrates the occurrence of some incident that has already happened concerning another incident.

The formula of Conditional Probability: Numerically, this may be interpreted as,

P(A|B) = N(A∩B)/N(B)

  • Here P(A) signifies the possibility that A has happened in a given B.
  • N(A no B) is the number of variables specific to both A and B.
  • N(B) is the number of variables in B that cannot be equivalent to 0.
  • Let N denote the cumulative number of things in the sampling space.

⇒P(A|B) = N(A∩B)NN(B)N

Because N(A ∩ B)/N and N(B)/N  represents the ratio of the number of desirable outcomes to the overall number of outcomes, the probability is implied.

 

Which are the probabilistic Events?

 

The probable event can be described as a collection of results of the experiment. In other terms, the probability case is the subset of the corresponding sampling field.

The Theorem of Bayes explains the probability of occurring in an incident linked to some situation. This is often called in the situation of uncertain probability.

When A and B are two events, the formula for Bayes Theorem shall be as follows:

P(A|B) = N(A∩B)/N(B); N(B)≠0

Here P(A) is the high probability of a situation when event A happens when event B is still occurring.

N(A ∩ B) is the number of factors specific both to A and B.

N(B) is the number of possibilities for B.

 

Probability Distribution:

 

The distribution of probabilities yields the potential results for random occurrence. It is also identified based on the associated sample space as a set of possible results for any random variable.

 

Random Variable:

 

Variables that indicate the potential outcomes of a random experiment are called random variables. They’re of two types:

  • Discrete Random factors.
  • Constant Random Factors.

Discrete random variables take only those distinct values that can be counted. However continuous random variables may have an endless number of potential outcomes.

 

Independent Events:

 

If the conditional probability of one event does not have an impact on the probability of yet another event, both events are considered to be independent of one another.

 

Mean:

 

The mean of the random variable is the sum of the random values of the potential outcomes of the random experiment.

 

Expected value: 

 

The expected meaning is the mean for a random variable. This is the expected value that is known for a random experiment.

Exercise Discussion of Xam Idea Class 12 Maths Solutions Chapter 14: Probability

Xam Idea 12 Maths Solutions for Probability have a total of 68 questions split into four segments.

Very Short Questions

  • This whole section will provide you with 8 problems, based primarily on the Xam Idea textbook. 
  • These questions will ask you to find the probability of two events (A and B). Here you will learn about probability and binomial distribution as well.

Short Answer Type Questions

  • In this category, you will have 8 problems with their solutions, which are resolved in the PYQ (Previous year questions) and OIQ (objective inventory questionnaires) components.
  • The PYQ part contains 3 questions based on the concepts of random probability and independent events.
  • The OIQ part comprises 5 questions. Here, you will be asked to apply the Bayes formula.

Long Answer Type Questions Part I

  • It has a total of 38 questions, covered in two sections, PYQ and OIQ.
  • The PYQ part contains 34 questions based on the concepts of the required probability and random variables.
  • The OIQ part comprises 4 questions that will ask you to find the probability of value “x” after observing the distribution table concerning the time given. Some problems are also based on Bayes theorem formula.

Long Answer Type Questions Part II

  • In this section, you will have 14 questions in the PYQ part and 4 questions in the OIQ part.
  • You will have questions on independent events and random probability distribution factors and fundamental probability principles. These questions are quite tricky to solve, you need to go through the respective formulas.

Why Use Xam Idea Class 12 Maths Solutions Chapter 14: Probability by instasolv?

  • Instasolv Xam Idea Class 12 Maths Solutions help you develop confidence in CBSE Class 12 Maths Probability to compete in the board exams.
  • These solutions will help you resolve your doubts and problems in an organized manner. You’re expecting to be ready to answer each problem in this chapter on your own.
  • When you’re finished with NCERT textbook, you should turn to our Xam Idea Class 12 Maths solutions because they have a good explanation and have been established by our topic experts using our CBSE syllabus. It is advisable to practice them before your exams.
  • You can access these Xam Idea Solutions for Class 12 without any cost.