1
GATE CSE 2024 Set 2
+1
-0.33

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

A

$\frac{1}{324}$

B

$\frac{5}{324}$

C

$\frac{7}{324}$

D

$\frac{11}{324}$

2
GATE CSE 2024 Set 1
+1
-0.33

Consider a permutation sampled uniformly at random from the set of all permutations of {1, 2, 3, ..., n} for some n ≥ 4. Let X be the event that 1 occurs before 2 in the permutation, and Y the event that 3 occurs before 4. Which one of the following statements is TRUE?

A

The events X and Y are mutually exclusive

B

The events X and Y are independent

C

Either event X or Y must occur

D

Event X is more likely than event Y

3
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+1
-0.33

Let A and B be two events in a probability space with $P(A) = 0.3$, $P(B) = 0.5$, and $P(A \cap B) = 0.1$. Which of the following statements is/are TRUE?

A

The two events A and B are independent.

B

$P(A \cup B) = 0.7$

C

$P(A \cap B^c) = 0.2$, where $B^c$ is the complement of the event B

D

$P(A^c \cap B^c) = 0.4$, where $A^c$ and $B^c$ are the complements of the events A and B respectively

4
GATE CSE 2019
Numerical
+1
-0.33
Two numbers are chosen independently and uniformly at random from the set {1, 2, ...., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ______.