1
GATE CSE 2024 Set 1
Numerical
+2
-0.66

A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is ________

2
GATE CSE 2023
MCQ (More than One Correct Answer)
+2
-0.67

Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

A
A and B are independent
B
A and C are independent
C
B and C are independent
D
Prob(B|C) = Prob(B)
3
GATE CSE 2021 Set 1
+2
-0.67

Consider the two statements.

S1 : There exist random variables X and Y such that

(E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y]

S2 : For all random variables X and Y,

Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]

Which one of the following choices is correct?

A
S1 is false, but S2 is true.
B
S1 is true, but S2 is false.
C

Both S1 and S2 are true.

D
Both S1 and S2 are false.
4
GATE CSE 2021 Set 1
Numerical
+2
-0.67
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 ______.