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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.
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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.
Consider f : {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f –1 and show that (f –1)–1 = f.
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
If f(x) = , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
The radius of an air bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?
A balloon, which always remains spherical, has a variable diameter
\begin{align} \frac{3}{2}(2x+1)\end{align}
Find the rate of change of its volume with respect to x.
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.