Choose the correct answer from the given four options. Two events… - Vidyadip

MCQ

Choose the correct answer from the given four options.
Two events E and F are independent. If $\text{P}(\text{E})=0.3,\text{P}(\text{E}\cup\text{F})=0.5,$ then $\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)-\text{P}\Big(\frac{\text{F}}{\text{E}}\Big)$ equal:

A
$\frac{2}{7}$
B
$\frac{3}{35}$
C
$\frac{1}{70}$
D
$\frac{1}{7}$

✓

Answer

$\frac{1}{70}$

Solution:

We have, $\text{P}(\text{E})=0.3,\text{P}(\text{E}\cup\text{F})=0.5$

Also E and F are independent.

Now $\text{P}(\text{E}\cup\text{F})=\text{P}(\text{E})+\text{P}(\text{F})-\text{P}(\text{E}\cap\text{F})$

$\Rightarrow0.5=0.3+\text{P}(\text{F})-0.3\text{P}(\text{F})$

$\Rightarrow\text{P}(\text{F})=\frac{0.5-0.3}{0.7}=\frac{2}{7}$

$\therefore\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)-\text{P}\Big(\frac{\text{F}}{\text{E}}\Big)$

$=\text{P}(\text{E})-\text{P}(\text{F})$ (as E and F are indepandent)

$=\frac{3}{10}-\frac{2}{7}=\frac{1}{70}$

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

More "M.C.Q (1 Marks)" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ and $B =\left[\begin{array}{rr}1 & - i \\ 0 & 1\end{array}\right]$, where $i =\sqrt{-1}$. If $M = A ^{ T } BA$, then the inverse of the matrix $AM ^{2023} A ^{ T }$ is $.........$

If f : R → R is given by f(x) = 3x - 5, then f^-1(x)

is given by $\frac{1}{3\text{x}-5}$
is given by $\frac{\text{x}+5}{3}$
does not exist because f is not one-one.
does not exist because f is not onto.

The region represented by the inequation system x, y ≥ 0, y ≤ 6, x + y ≤ 3 is:

The value of the definite integral,$\int\limits_1^\infty {{{({e^{x + 1}} + {e^{3 - x}})}^{ - 1}}\,dx} $ is

If $a$ and $b$ are chosen randomly from set $\{1,2 ,3,4,5,6\}$ with replacement. Then probability that $\mathop {\lim }\limits_{x \to 0} {\left( {\frac{{{a^x} + {b^x}}}{2}} \right)^{\frac{2}{x}}}=6$ is

If AB = A and BA = B, where A and B are square matrices, then:

B² = B and A² = A
B² ≠ B and A² = A
A² ≠ A, B² = B
A² ≠ A, B² ≠ B

$\int \limits_{\pi / 6}^{\pi / 3} \tan ^{3} x \cdot \sin ^{2} 3 x\left(2 \sec ^{2} x \cdot \sin ^{2} 3 x+3 \tan x \cdot \sin 6 x\right) d x$ is equal to

A particle moves along the curve $y = x^{3/2}$ in the first quadrant in such a way that its distance from the origin increases at the rate of $11$ units per second. The value of $\frac{{dx}}{{dt}}$ when $x = 3$ is

If ${2^x} + {2^y} = {2^{x + y}}$, then ${{dy} \over {dx}} = $

If $f(x) = \left\{ \begin{array}{l}x\sin \frac{1}{x},\,\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,k,\,\,x = 0\end{array} \right.$ is continuous at $x = 0$, then the value of $k$ is