If 2 P(A)=P(B)=5 13 and P(A B)=2 5 , then P ( A B )= __________ . - Vidyadip

MCQ

If $2 P(A)=P(B)=\frac{5}{13}$ and $P(A \mid B)=\frac{2}{5}$, then $P ( A \cup B )=$ __________ .

A
$\frac{10}{26}$
B
$\frac{10}{13}$
✓
$\frac{11}{26}$
D
$\frac{11}{13}$

✓

Answer

Correct option: C.

$\frac{11}{26}$

C

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 JUNE 2024→JUNE 2024 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\Gamma$ denote a curve $y = y ( x )$ which is in the first quadrant and let the point $(1,0)$ lie on it. Let the tangent to $\Gamma$ at a point $P$ intersect the $y$-axis at $Y_p$. If $P Y_p$ has length $1$ for each point $P$ on $\Gamma$, then which of the following options is/are correct?

$(1)$ $y=\log _0\left(\frac{1+\sqrt{1-x^2}}{x}\right)-\sqrt{1-x^2}$

$(2)$ $x y^{\prime}-\sqrt{1-x^2}=0$

$(3)$ $y=-\log _0\left(\frac{1+\sqrt{1-x^2}}{x}\right)+\sqrt{1-x^2}$

$(4)$ $x y^{\prime}+\sqrt{1-x^2}=0$

The value of the determinant $\begin{vmatrix} 5 &\text{amp; } 1 \\ 3 &\text{amp; } 2 \end{vmatrix}$

4
5
6
7

The value of c in Rolle's theorem for the function $\text{f}(\text{x})=\frac{\text{x}(\text{x}+1)}{\text{e}^{\text{x}}}$ defined on [-1, 0] is:

$0.5$
$\frac{1+\sqrt5}{2}$
$\frac{1-\sqrt5}{2}$
$-0.5$

Choose the correct answer from the given four options.
If A is a square matrix such that A² = I, then (A - I)³ + (A + I)³ - 7A is equal to:

A
I - A
I + A
3A

Match the statements/expressions in Column $I$ with the open intervals in Column $II$.

Column $I$	Column $II$
$(A)$ Interval contained in the domain of definition of non-zero solutions of the differential equation $(x-3)^2 y^{\prime}+y=0$	$(p)$ $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
$(B)$ Interval containing the value of the integral $\int_1^5(x-1)(x-2)(x-3)(x-4)(x-5) d x$	$(q)$ $\left(0, \frac{\pi}{2}\right)$
$(C)$ Interval in which at least one of the points of local maximum of $\cos ^2 x+\sin x$ lies	$(r)$ $\left(\frac{\pi}{8}, \frac{5 \pi}{4}\right)$
$(D)$ Interval in which $\tan ^{-1}(\sin x+\cos x)$ is increasing	$(s)$ $\left(0, \frac{\pi}{8}\right)$
	$(t)$ $(-\pi, \pi)$

If the function f : R → A given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then A =

R
[0, 1]
[0, 1)
[0, 1)

A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are ellegible. The probability that it came from LONDON is:

The general solution $y(x)$ of the differential equation $\frac{{d\left( {\int\limits_x^y {dt} } \right)}}{{dy}} = x$ , is

Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $\frac{d y}{d x}=2(y+2 \sin x-5) x-2 \cos x$ such that $\mathrm{y}(0)=7$. Then $\mathrm{y}(\pi)$ is equal to :

Which of the following function are strictly decreasing on $\left(0, \frac{\pi}{2}\right) ?$