Download App

Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
Evaluate $\text{P}(\text{A}\cap\text{B})\ \text{if}\ 2\text{P}(\text{A})=\text{P}(\text{B})=\frac{5}{13}\ \text{and}\ \text{P}(\text{A}|\text{B})=\frac{2}{5}.$
✓

Answer

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

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 "1 Marks Question" 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

If $\vec{\text{a}}, \text{ }\vec{\text{b}},\text{ } \vec{\text{c}}$ are unit vectors such that $\vec{\text{a}}, \text{ }\vec{\text{b}}, \text{ }\vec{\text{c}}\text{ }=\vec{0},$ then write the value of $\vec{\text{a}} \text{ . }\vec{\text{b}} + \vec{\text{b}} \text{ . } \text{ }\vec{\text{c}} +\vec{\text{c}} . \vec{\text{a}}\text{ }.$
→
Find $\int \sqrt{3-2 x-x^{2}} d x$
→
Find the value of x + y from the following equation:
$2\begin{bmatrix} \text{x} & 5 \\ 7 & \text{y - 3} \end{bmatrix} +\begin{bmatrix} 3 & -4 \\ 1 & 2 \\ \end{bmatrix}=\begin{bmatrix} 7 & 6 \\ 15 & 14 \\ \end{bmatrix}\dot{}$
→
Find the intervals in which the function f given by $f(x) = \sin x + \cos x,0 \leq x \leq 2\pi $ is increasing or decreasing.
→
Write the number of all possible matrices of order $2\times2$ with each entry 1, 2 or 3.
→
Probability of solving specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that exactly one of them solves the problem.
→
Find the equation of line passing through origin and parallel to $\mathrm{x}$-axis.
→
Classify the following as scalar and vector quantities.
Distance.
→
Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{\frac{1}{4}}+\text{x}^{\frac{1}{5}}=0.$
→
Integrate the functions in Exercises:
$\frac{(1+\log\text{x})^2}{\text{x}}$
→