If A and B are events such that P(A|B) = P(B|A), then - Vidyadip

Question

If A and B are events such that P(A|B) = P(B|A), then

✓

Answer

It is given that : P( A | B) = P( B | A)
$ \Rightarrow \frac{{P(A \cap B)}}{{P(B)}} = \frac{{P(B \cap A)}}{{P(A)}} $

$\Rightarrow \frac{1}{{P(B)}} = \frac{1}{{P(A)}} \Rightarrow P(A) = P(B) $

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 "1 Marks Question" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}}$ are such that, $|\vec{\text{a}}|=3,\ |\vec{\text{b}}|=\frac{2}{3}\ \text{and}\ \vec{\text{a}}\times\vec{\text{b}}$ is a unit vector, then write the angle between $\vec{\text{a}}\ \text{and}\ \vec{\text{b}}$.

In a box there are 4 white, 3 red and 5 black balls. Two balls are drawn, find the probability of getting two red balls.

P and Q are two points with position vectors 3$\overrightarrow{\text{a}}$ - 2$\overrightarrow{\text{b}}$ and $\overrightarrow{\text{a}} + \overrightarrow{\text{b}}$respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

If $\Delta=\left|\begin{array}{lll} {a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}} \end{array}\right|$ and $A_{ij}$ is Cofactors of $a_{ij},$ then value of $\Delta$ is given by

If $\text{|A}| = 3 \text{ and } \text{A}^{-1} = \begin{bmatrix} 3 & -1 \\ -\frac{5}{3} & \frac{2}{3} \\ \end{bmatrix},$ then write the adj A.

Find the area bounded by the curve $y=x$, the $x$-axis and the ordinates $x=0$ and $x=a$.

Let * be a binary operation on N given by a * b = HCF (a, b), a, b $\in$ N. Write the value of 22 * 4.

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.

Classify the following as scalar and vector quantities:
Velocity.

Integrate the functions in Exercises:
$\sqrt{\sin2\text{x}}\cos2\text{x}$