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
81
How is the product of the first 'n' natural numbers mathematically represented?
Answer:
1.2.3……(n-2) (n-1) (n)
The product of the first n natural numbers is defined as the factorial of n, denoted as n!. This is calculated by multiplying all positive integers from 1 up to n. Therefore, the sequence is 1 * 2 * 3 * ... * (n-1) * n. Option B correctly represents this sequence of multiplication. Note that the product does not include zero, as multiplying by zero would result in a product of zero for all n.
82
Which term defines the relationship between two events where the occurrence of one event precludes the occurrence of the other?
Answer:
Mutually exclusive
In probability theory, events are defined as mutually exclusive if they cannot occur simultaneously. If event A happens, event B cannot happen, and vice versa. This concept is fundamental in probability theory for calculating the likelihood of combined events and is a cornerstone of statistical analysis and set theory applications.
83
In probability theory, how are events that cannot occur simultaneously described?
Answer:
mutually exclusive events
Mutually exclusive events are defined as events that cannot happen at the same time. If one event occurs, the probability of the other occurring is zero.
84
In a standard deck of 52 playing cards, what is the probability of drawing either a diamond or a club?
Answer:
26/52=1/2
A standard deck contains 52 cards divided into four suits of 13 cards each. There are 13 diamonds and 13 clubs. Since these events are mutually exclusive, the probability of drawing a diamond or a club is the sum of their individual probabilities: 13/52 + 13/52 = 26/52, which simplifies to 1/2.
85
What is the term for an experiment that is repeated multiple times in sequence?
Answer:
Random
A random experiment is a process that can be repeated under similar conditions, where the outcome is not deterministic but belongs to a well-defined set of possible results. Repeated trials allow for the observation of long-term frequencies.
86
What term describes events that have the same probability of occurring?
Answer:
Equally likely events
Events are described as 'equally likely' if there is no reason to expect one event to occur more frequently than another. In a fair experiment, such as rolling a balanced die, each individual outcome has an equal probability of 1/6.
87
In set theory and probability, how is the joint event of two events G and H represented?
Answer:
G intersection H
A joint event occurs when two or more events happen simultaneously. In probability notation, the joint occurrence of events G and H is represented by the intersection of the two sets, denoted as G ∩ H. This signifies the set of outcomes that are common to both event G and event H.
88
In probability theory, if A and B are two events, how is the event representing the occurrence of A, B, or both denoted?
Answer:
A union B
The union of two events, denoted as A ∪ B, represents the set of all outcomes that are in A, in B, or in both. It captures the logical 'OR' condition in probability, encompassing all possibilities where at least one of the defined events occurs.
89
If the occurrence of one event precludes the possibility of another event happening simultaneously, what term describes these events?
Answer:
Mutually Exclusive
Events are defined as mutually exclusive if they cannot occur at the same time. In set theory, this means the intersection of the two events is the empty set. For example, when flipping a single coin, the outcomes 'Heads' and 'Tails' are mutually exclusive because the coin cannot land on both sides simultaneously. This is a fundamental concept in probability theory used to simplify the calculation of the probability of the union of events.
90
Given four machines with independent failure probabilities of 0.24, 0.45, 0.35, and 0.38, what is the probability that all four machines fail before the next year?
Answer:
0.168
Assuming the failure events are independent, the probability of all machines failing is the product of their individual probabilities: 0.24 * 0.45 * 0.35 * 0.38 = 0.014364. However, based on the provided answer key, there appears to be a discrepancy between the calculated result and the provided option. The calculation 0.24 * 0.45 * 0.35 * 0.38 equals approximately 0.0144, which does not match 0.168.