Download App

Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
Fill in the blanks.
If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
✓

Answer

If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then p $=\frac{1}{3}.$Solution:
Here, $\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9}$
$\because\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{\text{P}(\text{A}\cap\text{B})}{\text{P}(\text{B})}=\text{p}$
$\Rightarrow\text{P}(\text{A}\cap\text{B})=\frac{\text{p}}{3}$
And $\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
$\Rightarrow\frac{5}{9}=\text{p}+\frac{1}{3}-\frac{\text{p}}{3}$
$\Rightarrow\frac{5}{9}-\frac{1}{3}=\frac{2\text{p}}{3}$
$\Rightarrow\frac{5-3}{9}=\frac{2\text{p}}{3}$
$\Rightarrow\text{p}=\frac{2}{9}\times\frac{3}{2}=\frac{1}{3}$

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 "Fill In The Blanks[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

Fill in the blanks.
A feasible region of a system of linear inequalities is said to be _________, if it can be enclosed within a circle.
→
Fill in the blanks.
If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
→
Fill in the blank.
Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then gof = ______ and fog = ______.
→
If $A+B=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $A-2 B=\left[\begin{array}{cc}-1 & 1 \\ 0 & -1\end{array}\right]$, then $A$ $=$ _______
→
If A and B are two $3 \times 3$ order square matrix and $|A|=5,|B|=5$ then $|3 A B|=$ ________ .
→
Dfferentiation of $\cos (\sqrt{x})$ w.r.t. $x$ is ________ .
→
Fill in the blanks.
If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
→
Fill in the blanks:
Derivative of $x^2$ w.r.t. $x^3$ is _________.
→
Fill in the blanks:
If A is a matrix of order $3 × 3$, then $(A^2)^{-1} =$ ________.
→
Fill in the blanks.
If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
→