GATE CSE 2024 Set 1 | Probability Question 4 | Discrete Mathematics

GATE CSE 2024 Set 1

MCQ (More than One Correct Answer)

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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

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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 _____

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GATE CSE 2021 Set 1

Numerical

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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 ______.

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GATE CSE 2019

Numerical

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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 ______.

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