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
51
Under what condition is the special rule of multiplication of probability applicable?
Answer:
Independent
The special rule of multiplication states that for two events A and B, P(A and B) = P(A) * P(B). This rule is valid if and only if the events are independent, meaning the occurrence of one event does not affect the probability of the occurrence of the other.
52
In the context of probability experiments, how are the possible outcomes formally defined?
Answer:
events
In probability theory, an experiment is a process that leads to one of several possible outcomes. A subset of the sample space, which represents the set of all possible outcomes of an experiment, is referred to as an event. Events are the fundamental units used to assign probabilities.
53
Given two events Y and Z, how is the intersection of the occurrence of Z and the non-occurrence of Y denoted?
Answer:
Y-bar intersection Z
The non-occurrence of event Y is represented by the complement of Y, denoted as Y-bar (or Y'). The intersection of this complement with event Z represents the set of outcomes where Z occurs and Y does not occur, which is mathematically expressed as Y-bar ∩ Z.
54
What is the collective term for the set of all possible outcomes resulting from a random experiment?
Answer:
both b and c
The sample space is the set of all possible outcomes of a random experiment. In probability theory, an event is a subset of the sample space. Because the sample space itself is a set of outcomes, it is sometimes referred to as the event space in specific contexts, making both terms applicable depending on the theoretical framework used.
55
In a container holding 12 balls, where 6 are red and 6 are white, what is the probability of randomly selecting a white ball?
Answer:
6/12
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Here, there are 6 white balls out of a total of 12 balls. Therefore, the probability is 6/12, which simplifies to 0.5 or 50%.
56
What is the mathematical expression for the probability that an event A does not occur?
Answer:
1 – P(A)
According to the complement rule in probability theory, the sum of the probability of an event occurring and the probability of it not occurring is equal to 1. Therefore, the probability of the complement of event A, denoted as P(A'), is calculated as 1 minus the probability of event A.
57
If a single card is drawn from a standard 52-card deck, what is the probability of drawing either a five or a seven?
Answer:
8/52
In a standard deck, there are four fives and four sevens. Since these events are mutually exclusive (a card cannot be both a five and a seven), we add their individual probabilities: P(5) + P(7) = 4/52 + 4/52 = 8/52. This simplifies to 2/13, but 8/52 is the correct representation based on the provided options.
58
Which term describes a probability based on the relative frequency of an event occurring over a large number of repeated trials?
Answer:
empirical probability
Empirical probability, also known as experimental or relative frequency probability, is derived from the actual outcomes of an experiment. It is calculated by dividing the number of times an event occurs by the total number of trials conducted.
59
In a bag containing 4 white balls and 3 black balls, what is the probability of selecting a white ball in a single random draw?
Answer:
4 ⁄ 7
The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Here, there are 4 white balls and a total of 7 balls (4 white + 3 black). Therefore, the probability of drawing a white ball is 4 divided by 7.
60
What is the total number of outcomes in the sample space when flipping two coins simultaneously?
Answer:
4
When tossing two coins, each coin has two possible outcomes: Heads (H) or Tails (T). The total sample space is calculated by multiplying the possibilities for each coin (2 * 2), resulting in four possible outcomes: {HH, HT, TH, TT}. This represents the complete set of all possible results for the experiment.