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
1
Given that the probability of the intersection of two events A and B is 1/4, what is the probability of their union?
Answer:
1/3
The inclusion-exclusion principle states P(A∪B) = P(A) + P(B) - P(A∩B). Given P(A∩B) = 1/4, the calculation relies on the sum P(A) + P(B) being 7/12. Substituting these values into the formula yields 7/12 - 3/12 = 4/12, which simplifies to 1/3. This assumes the provided sum of individual probabilities is correct for the context.
2
What is the term for a collection of one or more outcomes resulting from a random experiment?
Answer:
Event
An event is formally defined as a subset of the sample space, which contains all possible outcomes of an experiment. When we perform an experiment, any specific outcome or group of outcomes that we are interested in is referred to as an event. This is a foundational concept in probability used to quantify uncertainty.
3
Which geometric shape is typically used in a Venn diagram to represent an event within a sample space?
Answer:
circle
Venn diagrams are visual tools used to represent sets and their relationships. In probability, the sample space is usually represented by a rectangle, while individual events are represented by circles or ovals within that rectangle. The area of the circle corresponds to the probability of the event occurring.
4
When rolling a fair, six-sided die, what is the probability of obtaining an even number?
Answer:
1/2
A standard six-sided die has the sample space {1, 2, 3, 4, 5, 6}. The even numbers in this set are {2, 4, 6}, totaling 3 favorable outcomes. The probability is the ratio of favorable outcomes to total outcomes, which is 3/6, simplifying to 1/2.
5
What is the term for a counting method where the arrangement or sequence of outcomes is considered significant?
Answer:
permutations
A permutation is an arrangement of items where the order is important. Unlike combinations, where the selection order does not matter, permutations account for the specific sequence in which elements are chosen or placed, making them essential for ordered counting problems.
6
What is the numerical value of the combination 5C5?
Answer:
1
The combination formula nCr is defined as n! / (r!(n-r)!). For 5C5, we substitute n=5 and r=5, resulting in 5! / (5!(5-5)!). Since 0! is defined as 1, the expression simplifies to 5! / (5! * 1), which equals 1. Intuitively, this represents the number of ways to choose 5 items out of a set of 5, which can only be done in exactly one way.
7
If a collection contains 40% dress shirts, 45% T-shirts, and 30% blue jeans, what is the probability of selecting a dress shirt?
Answer:
0.4
Probability is expressed as a value between 0 and 1. Given that 40% of the items are dress shirts, the probability of selecting one at random is 40 divided by 100, which equals 0.4. The other percentages provided are extraneous information for this specific calculation.
8
In probability theory, what term describes the set containing all possible outcomes of an experiment?
Answer:
collectively exhaustive events
A set of events is considered collectively exhaustive if at least one of the events must occur. When considering the entire sample space, the collection of all possible outcomes is collectively exhaustive because it covers every potential result of the experiment.
9
In the context of set theory, how are the sets of males (A) and females (B) in a town classified?
Answer:
Non-overlapping sets
In set theory, two sets are considered non-overlapping or disjoint if they share no common elements. Since an individual cannot be both male and female simultaneously in this classification, the intersection of set A and set B is the empty set. Therefore, they are mutually exclusive or non-overlapping.
10
When a fair coin is tossed once, what is the probability of the outcome being heads?
Answer:
1⁄2
A fair coin has two equally likely outcomes: heads and tails. The probability of any single specific outcome is the ratio of the number of favorable outcomes to the total number of possible outcomes. Thus, for heads, the probability is 1 divided by 2, or 1/2.