Download App

Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
If $\text{P}(\text{A}\cup\text{B})=0.8$ and $\text{P}(\text{A}\cap\text{B})=0.3$ then $\text{P}(\overline{\text{A}})=\text{P}(\overline{\text{B}})=$
  1. 0.3
  2. 0.5
  3. 0.7
  4. 0.9
✓

Answer

  1. 0.9

Solution:

If $\text{P}(\text{A}\cup\text{B})=0.8\text{ P}(\text{A}\cap\text{B})=0.3,$

$\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-\text{P}(\text{A}\cap\text{B})$

$\Rightarrow\ \text{P(A)}+\text{P(B)}=\text{P}(\text{A}\cup\text{B})-\text{P}(\text{A}\cap\text{B})$

$\Rightarrow\ \text{P(A)}+\text{P(B)}=1.1$

$\Rightarrow\ \text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=1-\text{P(A)}+1-\text{P(B)}$

$\Rightarrow\ \text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=\big[\text{P(A)}+\text{P(B)}\big]$

$\Rightarrow\ \text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=2-1.1$

$\Rightarrow\ \text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=0.9$

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 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 a matrix P has 8 elements then how many different values the order of the matrix can take?
  1. 3
  2. 4
  3. 8
  4. 6
→
If $sin(x + y)$ + $cos(2x + 2y)$ = $ln(3x + 3y)$, then $\frac{{dy}}{{dx}}$ is
→
Let $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}$ and $\vec{c}=\hat{j}-\hat{k}$ be three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ and $\vec{a} \cdot \vec{b}=1$. If the length of projection vector of the vector $\vec{b}$ on the vector $\vec{a} \times \vec{c}$ is $l$, then the value of $3l^{2}$ is equal to $.....$
→
Let $R\,= \{(x,y) : x,y \in N\, and\, x^2 -4xy +3y^2\, =0\}$, where $N$ is the set of all natural numbers. Then the relation $R$ is
→
If $ \overrightarrow{ a }=2 \hat{ i }+\hat{ j }+3 \hat{ k },  \overrightarrow{ b }=3 \hat{ i }+3 \hat{ j }+\hat{ k } $ and $\overrightarrow{ c }= c _{1} \hat{ i }+ c _{2} \hat{ j }+ c _{3} \hat{ k }$ are coplanar vectors and $\overrightarrow{ a } \cdot \overrightarrow{ c }=5, \overrightarrow{ b } \perp \overrightarrow{ c }$, then $122\left( c _{1}+ c _{2}+ c _{3}\right)$ is equal to.......
→
If ${I_1} = \int\limits_1^{\sin \theta } {\frac{x}{{1 + x^2}}} \,dx$ and ${I_2} = \int\limits_1^{\cos ec\theta } {\frac{{dx}}{{x\left( {{x^2} + 1} \right)}}}$; then the value of $\left| {\begin{array}{*{20}{c}}
  {{I_1}}&{I_1^2}&{{I_2}} \\ 
  {{e^{{I_1} + {I_2}}}}&{I_2^2}&{ - 1} \\ 
  1&{I_1^2 + I_2^2}&{ - 1} 
\end{array}} \right|$ is
→
Find the value of $\tan \frac{1}{2}\left[\sin ^{-1} \frac{2 x}{1+x^{2}}+\cos ^{-1} \frac{1-y^{2}}{1+y^{2}}\right]$, $|x|<1, y>0$ and $xy<1$
→
$\int_{}^{} {\frac{{{e^{{{\tan }^{ - 1}}x}}}}{{1 + {x^2}}}dx = } $
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two unit vectors inclined at an angle $\theta$, such that $\big|\vec{\text{a}}+\vec{\text{b}}\big|<1,$ then:
  1. $\theta<\frac{\pi}{3}$
  2. $\theta>\frac{2\pi}{3}$
  3. $\frac{\pi}{3}<\theta<\frac{2\pi}{3}$
  4. $\frac{2\pi}{3}<\theta<\pi$
→
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b ∈ T. Then, R is:
  1. Reflexive but not symmetric.
  2. Transitive but not symmetric.
  3. Equivalence.
  4. None of these.
→