Mechanical Engineering
GATE ME 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 27. Imported answers require independent review unless marked reviewed.
Question 39
Open questionMEMCQ2 marksNeeds review
A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administration selects three students from the council at random. What is the chance that out of the selected students, two belong to the same school and the third belongs to different school?
Your answerChoose one option.
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 5
Open questionGAMCQ1 markNeeds review
P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches and lost 5% of the matches.
If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?
Your answerChoose one option.
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 10
Open questionGAMCQ2 marksNeeds review
A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let
be the probability that she receives job offers from both the companies. Select the most appropriate option.Your answerChoose one option.
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 14
Open questionMEMCQ1 markNeeds review
If two unbiased coins are tossed, then what is the probability of having at least one head?
Your answerChoose one option.
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 5
Open questionGAMCQ1 markNeeds review
Take two long dice (rectangular parallelepiped), each having four rectangular faces labeled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the die is the score of the throw.
If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?
Your answerChoose one option.
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 44
Open questionMENAT2 marksNeeds review
Let
be a continuous random variable defined on
such that its probability density function
for
and 0 otherwise. Let
. Then the expected value of
is _____. (rounded off to 2 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 11
Open questionMEMCQ1 markNeeds review
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
Your answerChoose one option.
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 47
Open questionMENAT2 marksNeeds review
Let a random variable
follow Poisson distribution such that
The value of
is __________ (round off to 2 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 3
Open questionMEMCQ1 markNeeds review
The mean and variance, respectively, of a binomial distribution for
independent trials with the probability of success as
, areYour answerChoose one option.
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 5
Open questionMEMCQ1 markNeeds review
Consider a binomial random variable
. If
are independent and identically distributed samples from the distribution of
with sum
, then the distribution of
as
can be approximated asYour answerChoose one option.
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 answer