The probability that a student passes only in Hindi is 1/4. The probability of the student passes only in English is 5/9. The probability that the student passes in both of these subjects is 1/9. The probability that the student will pass in at least one of these two subjects is:
Show Hint
- 9/12
- 11/12
- 7/12
- 5/12
The Correct Option is B
Solution and Explanation
Step 1: Identify given probabilities.
• $P(\text{Hindi only}) = 1/4$
• $P(\text{English only}) = 5/9$
• $P(\text{Hindi} \cap \text{English}) = 1/9$
Step 2: Apply the addition rule for disjoint regions.
The event "passing at least one subject" is represented by: \[ P(H \cup E) = P(\text{Hindi only}) + P(\text{English only}) + P(\text{Hindi} \cap \text{English}) \] \[ P(H \cup E) = \frac{1}{4} + \frac{5}{9} + \frac{1}{9} \] \[ P(H \cup E) = \frac{1}{4} + \frac{6}{9} = \frac{1}{4} + \frac{2}{3} \]
Step 3: Calculate the final sum.
Find the common denominator (12): \[ P(H \cup E) = \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \]
Top CUET PG Civil Structural and Transport Engineering Questions
The solution(s) of the ordinary differential equation $y'' + y = 0$, is:
(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is:
- In a Binomial distribution, the sum of its mean and variance is $1.8$. If the event was conducted $5$ times, then the probability of two successes is:
Top CUET PG Soil Mechanics Questions
- The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesive soil satisfy the relation:
In a constant head permeameter, having cross-sectional area of $20 \, \text{cm}^2$, when the flow was taking place under a hydraulic gradient of $0.5$, the amount of water collected is $1200 \, \text{cm}^3$ in $60 \, \text{sec}$. The permeability of the soil is:
- To provide safety against piping failure, with a factor of safety as 3, what should be the maximum exit gradient for soil with a specific gravity of 2.5 and porosity of 0.35?
If the effective stress strength parameters are $C' = -10 \, \text{kPa}$ and $\phi' = 30^\circ$, the shear strength on a plane, within the saturated soil mass at a point where total normal stress is $300 \, \text{kPa}$ and pore water pressure is $150 \, \text{kPa}$, will be:
From a flow-net, which of the following information can be obtained?
A. Rate of flow
B. Pore water pressure
C. Exit gradient
D. Permeability
Choose the most appropriate answer from the options given below:
Top CUET PG Questions
- Given below are two statements:
Statement I: For Plato the meaning of the word 'Justice' is basically a conception in the mind only.
Statement II: For Plato the meaning of the word 'Justice' is fixed, mind-independently
In the light of the above statements, choose the correct answer from the options given below: - What is the electron count of OS6CO182-?
- XeF4 hydrolysis gives A + B, HF, and Oxygen. Find A and B
- What is more basic in pyrol and pyridine?
- Hydrolysis of Al2C3, Be2?