Download App

Probability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSProbability1 Mark
Question
Assertion $(A) :$ The probability that candidates $A$ and $B$ can solve the problem is $\frac{1}{5}$ and $\frac{2}{5}$, then probability that problem will be solved is given by $\frac{12}{25}$.
Reason $(R):$ If events $A \& B$ are independent, then $P(A \cap B)=P(A) \times P(B)$.
✓

Answer

$(d) :$ Probability of solving the problem by $A \ B$ is $=1-P($ None of them can solve the problem $)$
$=1-P(\bar{A} \cap \bar{B})=1-P(\bar{A}) \cdot P(\bar{B})$
$=1-[1-P(A)][1-P(B)]=1-\frac{4}{5} \times \frac{3}{5}=\frac{13}{25} .$

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 "Assertion (A) & Reason (B) MCQ" 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

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\cos^{-1}\text{x}=2\sin^{-1}\sqrt{\frac{1-\text{x}}{2}}=2\cos^{-1}\sqrt{\frac{1+\text{x}}{2}}.$
Reason: $1+\cos\text{A}=2\cos^{2}\big(\frac{\text{A}}{2}\big)$ and $1-\cos\text{A}=2\sin^{2}\big(\frac{\text{A}}{2}\big).$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
→
Assertion (A) : $B=\left[\begin{array}{llll}-\frac{1}{2} & \sqrt{5} & 2 & 3\end{array}\right]_{1 \times 4}$ is a row matrix.
Reason (R): If $B=\left[b_{i j}\right]_{1 \times n}$ is a row matrix, then its order is $n \times 1$.
→
Assertion (A) : If $A=\left(\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right)$, then $\operatorname{adj}(\operatorname{adj} A)=A$.
Reason (R) : $|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(n-1)^2}, A$ be $n$ rowed non singular matrix.
→
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as$:$
Assertion: If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
→
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If the matrix $\text{P}=\begin{pmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&3\end{pmatrix}$ is a symmetric matrix, then $\text{a}=-\frac{2}{3}$ and $\text{b}=-\frac{2}{3}.$
Reason: If P is a symmetric matrix, then P' = P.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
→
Assertion (A): Let $A=\{2,4,6\}$ and $B=\{3,5,7,9\}$ and defined a function $f=\{(2,3),(4,5),(6,7)\}$ from $A$ to B. Then, f is not onto.
Reason (R): A function $f$ : $A \rightarrow B$ is said to be onto, if every element of $B$ is the image of some elements of $A$ under $f$.
→
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: A relation R = {(1, 1), (1, 3), (1.5), (3, 1), (3, 3), (3,5} defined on the set A = {1, 3, 5} is transitive.
Reason: A relation R on the set A is symmetric $(\text{a},\text{b})\in\text{R}$ and $(\text{a},\text{c})\in\text{R}$
$\Rightarrow(\text{a},\text{c})\in\text{R}).$
  1. Both A and R are true and R is the correct explanation of A. 
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are fals.
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): :Consider the linear programming problem. Maximise Z = 4x + y Subject to constraints $\text{x}+\text{y}\leq50;\text{x}+\text{y}\geq100$ and $\text{x},\text{y}\geq0,$ Then, maximum value of Z is 50.
Reason (R): If the shaded region is bounded then maximum value of objective function can be determined.
  1. Both A and R are true and R is the correct explanation of A
  2. Both A and R are true but R is NOT the correct explanation of A
  3. A is true but R is false.
  4. A is false but R is true.
→
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $(\text{A}+\text{B})^{2}\neq\text{A}^{2}+2\text{AB}+\text{B}^{2}.$
Reason: Generally AB = BA.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
→
Assertion (A): $\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 7\end{array}\right]$ is a diagonal matrix.
Reason (R): $A=\left[a_{i j}\right]_{n \times n}$ is a square matrix such that $a_{i j}=0, \forall i \neq j$, then $A$ is called diagonal matrix.
→