Statistics MCQs
Topic Notes: Statistics
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
91
How are two events classified if their occurrence is linked or dependent on one another?
Answer:
compound events
In probability theory, a compound event is an event that is formed by combining two or more simple events. If the occurrence of one event affects the probability of the other, they are considered dependent, and their joint occurrence is a compound event.
92
In the context of a random experiment, what term is used to describe the individual observations or outcomes of a random variable?
Answer:
trials
A trial is a single performance of a random experiment. Each trial results in an outcome. When we observe a random variable across multiple repetitions of an experiment, each repetition is referred to as a trial, which contributes to the overall set of data points.
93
What is the probability of selecting a diamond card from a standard deck of 52 playing cards?
Answer:
13/52
A standard deck contains 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Therefore, the probability of drawing a diamond is the number of diamond cards (13) divided by the total number of cards (52), which simplifies to 1/4.
94
When flipping a fair coin, what is the probability of obtaining a head?
Answer:
Fifty %
A fair coin has two possible outcomes: heads or tails. Since each outcome is equally likely, the probability of getting heads is 1 out of 2, which is 0.5 or 50%. This represents the total probability space for a single coin flip.
95
What is the probability of obtaining an odd sum when rolling two fair dice?
Answer:
18/36
When rolling two dice, there are 6 * 6 = 36 possible outcomes. A sum is odd if one die is even and the other is odd, or vice versa. There are 18 such combinations (e.g., 1+2, 1+4, 1+6, 2+1, 2+3, 2+5, etc.). Since 18 out of 36 outcomes result in an odd sum, the probability is 18/36, which simplifies to 1/2.
96
What is an outcome of an experiment called if it cannot be decomposed into smaller, more specific outcomes?
Answer:
simple event
A simple event, also known as an elementary event, is an outcome that cannot be broken down into further, more granular outcomes. It represents a single point in the sample space of a random experiment.
97
Which mathematical principles are essential for calculating the number of possible outcomes in an experiment?
Answer:
all of above
Counting rules, including permutations (where order matters) and combinations (where order does not matter), are fundamental to probability theory. These methods allow for the systematic calculation of the total number of outcomes in complex experiments, which is necessary for determining probabilities.
98
How is the probability of an event calculated using the classical definition?
Answer:
probability of an event
According to the classical definition of probability, the probability of an event is the ratio of the number of favorable outcomes to the total number of equally likely outcomes in the sample space of the experiment.
99
What is the probability of obtaining exactly three tails when tossing three balanced coins once?
Answer:
1/8
When tossing three coins, the total number of possible outcomes is 2^3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. The event 'exactly three tails' corresponds to only one outcome: {TTT}. Since there is only 1 favorable outcome out of 8 equally likely possibilities, the probability is 1/8.
100
How many fundamental properties are common to all statistical experiments?
Answer:
Two
In the context of probability theory, a random experiment is generally defined by two core properties: the experiment can be repeated under identical conditions, and the outcome of any specific trial cannot be predicted with certainty, though the set of all possible outcomes is known.