The Mathematics of Maybe: Introduction to Probability MCQs for UPSC Prelims
120 practice questions covering The Mathematics of Maybe: Introduction to Probability, organised into 0 topics.
120 questions include a written explanation.
Pick a topic below, or try the samples first.
Sample questions
Q1
hard
In a survey of $400$ families in a colony, $260$ owned a car. Of the surveyed families that owned no car, exactly half owned a two-wheeler. The colony has $1600$ families in all. Using these estimates, how many families in the colony own neither a car nor a two-wheeler?
A$140$
B$280$
C$560$
D$1040$
Show answer and explanation
Correct answer: B - $280$
In the sample $400 - 260 = 140$ families had no car, an estimated probability of $\frac{140}{400} = 0.35$, so about $0.35 \times 1600 = 560$ colony families own no car. Half of those own a two-wheeler, leaving $\frac{560}{2} = 280$ families with neither. The value $560$ stops one step early, $1040$ is the predicted number of car owners, and $140$ is the sample's own count of families without a car.
Q2
easy
A factory makes $20000$ bulbs in a week and tests $200$ of them for faults. Which group is the sample in this study?
AAll $20000$ bulbs made during the week
BThe $200$ bulbs that were tested
CThe machines used in the factory
DThe bulbs that turned out to be faulty
Show answer and explanation
Correct answer: B - The $200$ bulbs that were tested
A sample is the smaller group actually examined, so the $200$ tested bulbs are the sample. All $20000$ bulbs form the population, the group the factory wants a conclusion about. The faulty bulbs are a result found by the testing rather than the group tested, and the machines are equipment, not items being studied.
Q3
easy
According to the Law of Large Numbers, what happens to the experimental probability of a result as a fair experiment is repeated more and more times?
AIt settles closer and closer to the theoretical probability.
BIt becomes exactly equal to the theoretical probability once $100$ trials are done.
CIt moves further and further away from the theoretical probability.
DIt stops changing after the first few trials.
Show answer and explanation
Correct answer: A - It settles closer and closer to the theoretical probability.
The Law of Large Numbers says that as the number of trials increases without limit, the experimental probability draws closer and closer to the theoretical value. It promises no exact match at any fixed number of trials such as $100$, and the value keeps shifting a little with every extra trial rather than freezing early. Moving away from the theoretical value is the opposite of what happens.
Q4
easy
A shop sells shirts in $3$ colours and caps in $2$ colours. A tree diagram is drawn to show every possible shirt-and-cap pair. How many complete paths does the tree have?
A$6$
B$9$
C$3$
D$5$
Show answer and explanation
Correct answer: A - $6$
Each of the $3$ shirt colours branches into the $2$ cap colours, so the tree ends in $3 \times 2 = 6$ complete paths, one for each pair. Adding the counts gives $5$, which counts garments rather than pairs. The value $3$ counts the shirts only, and $9$ would be right if there were three cap colours as well.
Q5
easy
(A) Tossing a coin and then rolling a die, recording both results, is a multi-step experiment. (R) The experiment is carried out in two stages, and each stage has its own set of outcomes.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: A - Both A and R are true, and R is the correct explanation of A
(A) is true: the coin toss and the die roll are two separate stages of one experiment. (R) is true as well, and being carried out in stages, each with its own outcomes, is exactly what makes an experiment multi-step, so (R) explains (A). Neither statement is false, and the connection between them is a real one.
Q6
easy
A newspaper wants to know what fraction of the $60000$ voters in a town support a new bus route, so it questions $500$ of them. In this survey, what is the population?
AThe reporters who carried out the survey
BOnly the voters who support the new bus route
CAll $60000$ voters in the town
DThe $500$ voters who were questioned
Show answer and explanation
Correct answer: C - All $60000$ voters in the town
The population is the whole group the survey is trying to describe, which here is all $60000$ voters. The $500$ voters actually questioned form the sample, a part of the population chosen to stand for it. The supporters are one kind of response rather than the group being studied, and the reporters are not being surveyed at all.
Practice the full The Mathematics of Maybe: Introduction to Probability bank free
All 120 questions with timed practice, instant scoring, and explanations. Free forever.