Evaluate P ( A B ) if 2P(A) = P (B) = 5 13 and P ( A|B ) = 2 5 - Vidyadip

Question

Evaluate ${P\left( {A \cup B} \right)}$ if 2P(A) = P (B) = $\frac{5}{{13}}$ and $P\left( {A|B} \right) = \frac{2}{5}$

✓

Answer

Given: 2 P(A) = P (B) = $\frac{5}{{13}}$, $P\left( {A|B} \right) = \frac{2}{5}$
$\therefore $ P (A) = $\frac{5}{{26}}$
Now, $P\left( {A \cap B} \right) = P\left( {B|A} \right)$ . P (B) = $\frac{2}{5} \times \frac{5}{{13}} = \frac{2}{{13}}$
and $P\left( {A \cup B} \right)$ = P(A) + P (B) – $P\left( {A \cap B} \right)$ = $\frac{5}{{26}} + \frac{5}{{13}} - \frac{2}{{13}} = \frac{{11}}{{26}}$

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 "2 Marks Questions" 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

Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $Z^+$ define $*$ by $a * b = |a - b|$
Here$, Z^+$ denotes the set of all non$-$negative integers.

The following defines a relation on N:
$\text{x}>\text{y, x, y}\in\text{N}$
Determine which of the above relations are reflexive, symmetric and transitive.

Find the second order derivatives of the function given in Exercise:
$\text{e}^\text{x}\sin5\text{x}$

A fair coin is tossed 8 times, find the probability of.
at least six heads.

A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that.
exactly two bulbs are defective.

If $\text{y}=\cot\text{x}$ show that $\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\text{y}\frac{\text{dy}}{\text{dx}}=0$

Determine whether the following operations define a binary operation on the given set or not:$'\odot'$ on N defined by $\text{a}\odot\text{b}=\text{a}^{\text{b}}+\text{b}^{\text{a}}$ for all $\text{a, b}\in\text{N.}$

Write a value of $\int\text{a}^{\text{x}}\text{e}^{\text{x}}\text{ dx}$

Find the values of x, y and z so that the vectors $\vec{a}=x \hat{i}+2 \hat{j}+z \hat{k}$ and $\vec{b}=2 \hat{i}+y \hat{j}+\hat{k}$ are equal.

If $\begin{bmatrix}\text{x}+3&\text{z}+4&2\text{y}-7\\4\text{x}+6&\text{a}-1&0\\\text{b}-3&3\text{b}&\text{z}+2\text{c}\end{bmatrix}=\begin{bmatrix}0&6&3\text{y}-2\\2\text{x}&-3&2\text{c}-2\\2\text{b}+4&-21&0\end{bmatrix}$ Obtain the values of a, b, c, x, y and z.