NCERT Solutions for Class 12 Chapter 13 Probability Exercise 13.4

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Class 12 Maths NCERT Solutions Chapter 13 Probability Exercise 13.4 is based on Random Variables and its Probability Distributions. Key topics covered under these concepts are:

Probability distribution of a random variable
Mean and variance of a random variable

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Also Read:

Chapter 13 Probability Important Topics
Conditional Probability	Conditional Probability Formula	Multiplication Theorem on Probability
Bias	Independent Events	Mean and variance of random variable
Difference between mutually exclusive and independent events	Uniform distribution formula	T distribution formula
Coin toss probability formula	T distribution	Uniform distribution
Probability and statistics symbols	Probability density function	Geometric distribution
Exponential distribution	Beta distribution	NCERT Solutions for Class 12 Mathematics Chapter 13 Probability

Also Read:

Class 12 Mathematics Important Guides
Class 12 Mathematics Notes	Math MCQs	Trigonometry
Number Systems	Probability and Statistics	Arithmetic
Algebra	Difference Between Topics in Maths	Math Study Guides
Math Formula	NCERT Solutions for Class 12 Maths	Mensuration

CBSE CLASS XII Related Questions

1.
The probability that a student buys a colouring book is 0.7, and a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find:
(i) The probability that she buys both the colouring book and the box of colours.
(ii) The probability that she buys a box of colours given she buys the colouring book.
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2.
Prove that:
\( \tan^{-1}(\sqrt{x}) = \frac{1}{2} \cos^{-1}\left( \frac{1 - x}{1 + x} \right), \quad x \in [0, 1] \)
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3.
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).
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4.
The domain of the function \( f(x) = \cos^{-1}(2x) \) is:
- \([-1, 1]\)
- \(\left[0, \frac{1}{2}\right]\)
- \([-2, 2]\)
- \(\left[-\frac{1}{2}, \frac{1}{2}\right]\)
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5.
Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
\[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.
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6.
If \( \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \), then prove that \( \frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} \).
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