1
GATE CE 2025 Set 2
MCQ (More than One Correct Answer)
+1
-0
Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?
A
$P(A \cap B)=P(A) P(B)$, if $A$ and $B$ are mutually exclusive.
B
Conditional probability, $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=1$ if $\mathrm{B} \subset \mathrm{A}$.
C
$P(A \cup B)=P(A)+P(B)$, if $A$ and $B$ are mutually exclusive.
D
$P(A \cap B)=0$, if $A$ and $B$ are independent.
2
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33

$X$ is the random variable that can take any one of the values, $0,1,7,11$ and 12 . The probability mass function for $X$ is

$$ \begin{aligned} & \mathrm{P}(X=0)=0.4 ; \mathrm{P}(X=1)=0.3 ; \mathrm{P}(X=7)=0.1 ; \\ & \mathrm{P}(X=11)=0.1 ; \mathrm{P}(X=12)=0.1 \end{aligned} $$

Then, the variance of $X$ is

A
20.81
B
28.40
C
31.70
D
10.89
3
GATE CE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the student will pass in at least one of these two subjects is

A

$\frac{17}{18}$

B

$\frac{11}{18}$

C

$\frac{14}{18}$

D

$\frac{1}{18}$

4
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Which of the following probability distribution functions (PDFs) has the mean greater than the median?

GATE CE 2023 Set 2 Engineering Mathematics - Probability and Statistics Question 6 English
A
Function 1 
B
Function 2
C
Function 3
D
Function 4
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