Download App

STD 12 - 13. probability — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 13. probability1 Mark
MCQ
Let $E_{1}$ and $E_{2}$ be two events such that the conditional probabilities $P \left( E _{1} \mid E _{2}\right)=\frac{1}{2}$, $P \left( E _{2} \mid E _{1}\right)=\frac{3}{4}$ and $P \left( E _{1} \cap E _{2}\right)=\frac{1}{8}$. Then
  • A
    $P \left( E _{1} \cap E _{2}\right)= P \left( E _{1}\right) \cdot P \left( E _{2}\right)$
  • B
    $P \left( E _{1}^{\prime} \cap E _{2}^{\prime}\right)= P \left( E _{1}^{\prime}\right) \cdot P \left( E _{2}\right)$
  • ✓
    $P \left( E _{1} \cap E _{2}^{\prime}\right)= P \left( E _{1}\right) \cdot P \left( E _{2}\right)$
  • D
    $P \left( E _{1}^{\prime} \cap E _{2}\right)= P \left( E _{1}\right) \cdot P \left( E _{2}\right)$
✓

Answer

Correct option: C.
$P \left( E _{1} \cap E _{2}^{\prime}\right)= P \left( E _{1}\right) \cdot P \left( E _{2}\right)$
c
(A) $P \left( E _{1}\right) \cdot P \left( E _{2}\right)=\frac{1}{6} \cdot \frac{1}{4}=\frac{1}{24} \neq P \left( E _{1} \cap E _{2}\right)$

(B) $P \left( E _{1}^{\prime} \cap E _{2}^{\prime}\right)=1- P \left( E _{1} \cup E _{2}\right)$

$=1-\left( P \left( E _{1}\right)+ P \left( E _{2}\right)- P \left( E _{1} \cap E _{2}\right)\right)$

$=1-\left(\frac{1}{6}+\frac{1}{4}-\frac{1}{8}\right)=\frac{17}{24}$

$P \left( E _{1}^{\prime}\right) P \left( E _{2}\right)=\frac{5}{6} \times \frac{1}{4}=\frac{5}{24}$

(C) $P \left( E _{1} \cap E _{2}^{\prime}\right)= P \left( E _{1}\right)- P \left( E _{1} \cap E _{2}\right)=\frac{1}{6}-\frac{1}{8}=\frac{1}{24}$

(D) $P \left( E _{1}^{\prime} \cap E _{2}\right)= P \left( E _{2}\right)- P \left( E _{1} \cap E _{2}\right)=\frac{1}{4}-\frac{1}{8}=\frac{1}{8}$

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 STD 12 - 13. probability→STD 12 - 13. probability — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\mid\text{a}\mid=4$ and $-3\underline{<}\lambda\underline{<}2$ then the range of $\mid\lambda\text{a}\mid$ is:
→
Choose the correct answer from the given four options.
Let $f : [0, 1] \rightarrow [0, 1]$ be defined by $\text{f}(\text{x})=\begin{cases}\text{x, if x is rational}1-\text{x, if x is irrational}\end{cases}\}$ Then $\text{(fof)x}$ is:
→
The solution of $\frac{\text{d}^2\text{y}}{\text{dx}^2}=0$ represents:
→
$\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}\,dx = } $
→
If $f : R \to R,$ be a continuous function such that $f(x) = \int\limits_1^x {tf(t)dt,}$ then the correct statement is -
→
If $A = \left[ {\begin{array}{*{20}{c}}{1/3}&2\\0&{2x - 3}\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}3&6\\0&{ - 1}\end{array}} \right]$and $AB = I$, then $x =$
→
Let $A=\left[\begin{array}{l}a_{1} \\ a_{2}\end{array}\right]$ and $B=\left[\begin{array}{l}b_{1} \\ b_{2}\end{array}\right]$ be two $2 \times 1$ matrices with real entries such that $A = XB,$

where $X=\frac{1}{\sqrt{3}}\left[\begin{array}{cc}1 & -1 \\ 1 & k\end{array}\right],$ and $k \in R$. If $a _{1}^{2}+ a _{2}^{2}=\frac{2}{3}\left( b _{1}^{2}+ b _{2}^{2}\right)$ and $\left( k ^{2}+1\right) b _{2}^{2} \neq-2 b _{1} b _{2}$ then the value of $k$ is ....... .

→
For two events $A$ and $B$, if $P(A) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}$ and $P\,\left( {\frac{B}{A}} \right) = \frac{1}{2},$ then
→
If the function f : R → A given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then A =
→
The differential equation of all the lines in the $xy$-plane is
→