Probability and Statistics Lecture 1

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Questions and Answers

What is the definition of probability?

A measure of certainty

The frequency of an event

The number of possible outcomes

A measure of uncertainty (correct)

What is a sample space?

The set of all possible outcomes of an experiment (correct)

The probability of an event

A single outcome of an experiment

A subset of all possible outcomes

What is an event in probability?

A subset of a sample space (correct)

A single outcome of an experiment

The probability of an event

The set of all possible outcomes

What is a simple event?

An event containing only one outcome Signup and view all the answers

What is a compound event?

An event containing more than one outcome Signup and view all the answers

What is the complement of an event?

The event not occurring Signup and view all the answers

What are mutually exclusive events?

Events that cannot occur together Signup and view all the answers

What is the total number of people in the group?

200 Signup and view all the answers

In the experiment of rolling a die, what is the event 'A or B'?

The event of getting a prime number or an odd number Signup and view all the answers

How many people have type AB blood?

15 Signup and view all the answers

What is the probability that a person selected at random has O blood type?

7/20 Signup and view all the answers

How many students like Mathematics in the survey?

40 Signup and view all the answers

How many students like both Mathematics and English?

10 Signup and view all the answers

How many students like all three subjects in the survey?

5 Signup and view all the answers

What is a Venn diagram used to represent?

Differences and similarities between two concepts Signup and view all the answers

What does P(E) or Pr(E) denote?

Probability of event E Signup and view all the answers

What is the formula for determining probability using the classical method?

P(E) = number of outcomes in the event / total number of outcomes Signup and view all the answers

What are two events that do not depend on each other?

Independent events Signup and view all the answers

What is the rule that states P(S) = 1?

Axiom 2 Signup and view all the answers

What is the probability of an event that is certain to occur?

1 Signup and view all the answers

What is the probability of rolling an even number on a die?

1/2 Signup and view all the answers

What is the probability of obtaining two heads when two coins are tossed?

1/4 Signup and view all the answers

Study Notes

Probability

Probability is a measure of uncertainty
Sample Space: Set of all possible outcomes of an experiment

Events

An event is a subset of a sample space of some experiment
Simple Event: An event containing only one outcome
Compound Event: An event containing more than one outcome

Event Operations

Complement
Intersection
Mutually Exclusive Events: If event A and B cannot occur together
Union

Venn Diagrams

Used to visually represent the differences and similarities between two concepts
Typically uses intersecting and non-intersecting circles

Axioms of Probability

Axiom 1: For any event, P(A) ≥ 0
Axiom 2: P(S) = 1, where S is the sample space

Determining Probability

Classical Method: P(E) = Number of outcomes in the event / Total number of outcomes in the sample space

Independent Events

Let's say we have two events A and B
If the occurrence of A does not depend on the occurrence of B

Rules of Probability

Complement Rule
Addition and Multiplication Rule

Probability Problems

Rolling a die: Find the probability that an even number is obtained
Two coins are tossed: Find the probability that two heads are obtained
Person selected at random: Find the probability that this person has O blood type
Survey of students: Find the probability that a student selected likes Mathematics or Science, etc.

Exercise

Students like Mathematics, Science, and English: Find the probability of various events

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Description

This quiz covers the basics of probability, Venn diagrams, and statistics, as part of the CS 1212 and IT 1213 course. Test your understanding of these fundamental concepts in computer science and IT.