Chemical Engineering
GATE CH topic:probability-and-statistics PYQs
Build your understanding with focused practice from past exam papers.
How to practice 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 15. Imported answers require independent review unless marked reviewed.
Question 34
Open questionCHNAT1 markNeeds review
An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:
Event A: The outcome of the rolled die is a prime number.
Event B: The outcome of the rolled die is an odd number less than 4.
The conditional probability of A given B, denoted by P (A|B), is ______ (rounded off to one decimal place).
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Open questionCHMCQ1 markNeeds review
A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is
Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 37
Open questionCHMCQ2 marksNeeds review
A probability distribution function is given as
where
is a positive constant. For a function
, the expectation of
isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 12
Open questionCHMCQ1 markNeeds review
Consider the normal probability distribution function
If
and
are the mean and standard deviation of
respectively, then the ordered pair
isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 36
Open questionCHMCQ2 marksNeeds review
An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons
and
entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 7
Open questionGAMCQ2 marksNeeds review
A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown.
Two such disks are used in a game where their arrows are independently spun.
What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 8
Open questionGAMCQ2 marksNeeds review
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.
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Open questionCHNAT1 markNeeds review
A source placed at the origin of a circular sample holder (radius
) emits particles uniformly in all directions. A detector of length
has been placed along the perimeter of the sample holder. During an experiment, the detector registers 14 particles.The total number of particles emitted during the experiment is __________.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 35
Open questionCHNAT2 marksNeeds review
The probability distribution function of a random variable
is shown in the following figure.
From this distribution, random samples with sample size
are taken. If
is the sample mean, the standard deviation of the probability distribution of
, i.e.
is ________ (round off to 3 decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 26
Open questionCHMCQ2 marksNeeds review
In a box, there are 5 green balls and 10 blue balls. A person picks 6 balls randomly. The probability that the person has picked 4 green balls and 2 blue balls is
Your answerChoose one option.
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