Let be the sample space and A be an event. Given below are two st… - Vidyadip

MCQ

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements :

$(S1)$ : If $P ( A )=0$, then $A =\phi$

$( S 2)$ : If $P ( A )=$, then $A =\Omega$

Then

A
only $(S1)$ is true
B
only $(S2)$ is true
C
both $(S1)$ and $(S2)$ are true
✓
both $(S1)$ and $(S2)$ are false

✓

Answer

Correct option: D.

both $(S1)$ and $(S2)$ are false

d
$\Omega=$ sample space

$A =$ be an event

If $P(A)=0 \Rightarrow A=\phi$

If $P ( A )=1 \Rightarrow A =\Omega$

Then both statement are true

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The coefficients $a, b, c$ in the quadratic equation $ax ^2+ bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$. The probability of this equation having repeated roots is :

Let $P$ be a point on the ellipse $\frac{ x ^2}{9}+\frac{ y ^2}{4}=1$. Let the line passing through $P$ and parallel to $y -$axis meet the circle $x^2+y^2=9$ at point $Q$ such that $P$ and $Q$ are on the same side of the $x-$axis. Then, the eccentricity of the locus of the point $R$ on $P Q$ such that $P R: R Q=4: 3$ as $P$ moves on the ellipse, is $:$

Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?

If $a,b,c$ are positive integers, then the determinant $\Delta = \left| {\,\begin{array}{*{20}{c}}{{a^2} + x}&{ab}&{ac}\\{ab}&{{b^2} + x}&{bc}\\{ac}&{bc}&{{c^2} + x}\end{array}\,} \right|$ is divisible by

Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

The period of the function $f\left( x \right)$ = $\frac{x}{3} - \left[ {\frac{x}{3} - 5} \right] + \frac{x}{4} - \left[ {\frac{x}{4} - 5} \right] + \frac{x}{5} - \left[ {\frac{x}{5} - 5} \right]$ is (where $[.]$ is $G.I.F.$ )

$A =\{ x_1, x_2, x_3, x_4 \}; \,\,$$B = \{ y, y_2, y_3, y_4 \} .$ A function is defined from set $A$ to set $B.$ Number of one-one function such that $f(x_i) \ne y_i$ for $i = 1, 2, 3, 4$ is equal to :

If $f (x) = \cos(\tan^{-1}x)$ then the value of the integral $\int\limits_0^1 {x\,\,f\,''(x)} \,\,dx$ is

A man takes a step forward with probability $0.4$ and backward with probability $0.6.$ The probability that at the end of eleven steps he is one step away from the starting point is

The expansion of $\frac{1}{{{{(4 - 3x)}^{1/2}}}}$ binomial theorem will be valid, if