GATE CSE 2024 Set 1 | Probability Question 3 | Discrete Mathematics

GATE CSE 2024 Set 1

MCQ (Single Correct Answer)

-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?

The events X and Y are mutually exclusive

The events X and Y are independent

Either event X or Y must occur

Event X is more likely than event Y

GATE CSE 2024 Set 1

MCQ (More than One Correct Answer)

-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?

The two events A and B are independent.

$P(A \cup B) = 0.7$

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

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

GATE CSE 2021 Set 2

Numerical

-0

For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is _____

Your input ____

GATE CSE 2021 Set 1

Numerical

-0

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that, its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.

Your input ____