GATE CSE topic:probability-and-statistics PYQs & Answers

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topic:probability-and-statistics

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 21. Imported answers require independent review unless marked reviewed.

Topic practice 21 questionsPage 1 of 3

A fair six-faced dice, with the faces labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, is rolled thrice. What is the probability of rolling ‘6’ exactly once?

Your answerChoose one option.

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A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability

and for a fake coin,

. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is ______. (rounded off to two decimal places)

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Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is 0.01. Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is _____. (rounded off to three decimal places)

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Consider a probability distribution given by the density function

The probability that

lies between 2 and 3, i.e.,

is __________. (rounded off to three decimal places)

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The unit interval (0,1) is divided at a point chosen uniformly distributed over (0,1) in ℝ into two disjoint subintervals.

The expected length of the subinterval that contains 0.4 is __________. (rounded off to two decimal places)

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

Your answerChoose one option.

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Let

and

be two events in a probability space with

, and

. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The two events

and

are independent

, where

is the complement of the event

, where

and

are the complements of the events

and

, respectively

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Let

and

be random variables, not necessarily independent, that take real values in the interval

. Let

and let the mean values of

, respectively. Which one of the following statements is TRUE?

Your answerChoose one option.

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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 ________.

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There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ____________

Your answerChoose one option.

0.3024

0.4235

0.6976

0.8125

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GATE CSE topic:probability-and-statistics PYQs

How to practice topic:probability-and-statistics

Question 8

Question 32

Question 56

Question 58

Question 65

Question 18

Question 27

Question 44

Question 63

Question 8