
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 (EF) and P(FE). Ans: It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2
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 of NCERT Solutions for Class Mathematics Chapter 13 Probability
Download pdf of NCERT Examplar with Solutions for Class Mathematics Chapter 13 Probability
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 (EF) and P(FE). 
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 oneone, 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 + x^{2 }
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 oneone nor onto, where [x] denotes the greatest integer less than or equal to x.
Determine order and degree(if defined) of differential equation y' + 5y = 0
Determine order and degree(if defined) of differential equation
\begin{align}\left(\frac{d^2y}{dx^2}\right)^2\;+\;cos\left(\frac{dy}{dx}\right)\;=\;0\end{align}
Represent graphically a displacement of 40 km, 30° east of north.
In each of the following cases, state whether the function is oneone, 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 + x^{2 }
In Figure, identify the following vectors.
(i) Coinitial (ii) Equal (iii) Collinear but not equal
Show that the Signum Function f : R → R, given by
is neither oneone nor onto.