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Q1 Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Ans: It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2
Welcome to the Chapter 13 - Probability, Class 12 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 13 - Probability.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics Events, axiomatic probability, mutually exclusive events, probability of ‘not’, ‘and’, and ‘or’ events. and excel in their exams. By going through these Probability question answers, you can strengthen your foundation and improve your performance in Class 12 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
In this chapter, we will learn some new aspects of probability like conditional probability etc. All the concepts which we have studied in previous classes will help us in understanding these new topics in a better way. Topics which are included in this chapter - conditional probability, multiplication theorem on probability, independent events, Bayes theorem, total probability, random variable and its probability distribution, mean and variance, Binomial distribution.
Download PDF - Chapter 13 Probability - Class 12 Mathematics
Download PDF - NCERT Examplar Solutions - Chapter 13 Probability - Class 12 Mathematics
Q1 | Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E). |
Ans: | It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2 |
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
In Figure, identify the following vectors.
(i) Coinitial (ii) Equal (iii) Collinear but not equal
Represent graphically a displacement of 40 km, 30° east of north.
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
Classify the following as scalar and vector quantities.
(i) time period (ii) distance (iii) force
(iv) velocity (v) work done