Introduction to probability

Question 1

What is probability?

Answer 1

Mathematics of “random experiments”

Question 2

Ingredients of random experiments

Answer 2

1 - Set
2 - Probability

Question 3

SET

Answer 3

The set contains all possible outcomes of the experiments.
Called “Sample space”.
Denoted by “S”

Question 4

EVENTS

Answer 4

The subsets of a set are called events.

• If A is an event, then A is a subset of S
• If A is an event,
  A° = S - A –> A° is a complement of A

Question 5

A and B are events

Answer 5

• A∩B = {s ϵ S: s ϵ A, s ϵ B}
• AUB = {s ϵ S: s ϵ A or s ϵ B}

Question 6

A PROBABILITY

Answer 6

A probability is a way of assigning to each event A a number P(A) (probability of A) in such a way the following properties are satisfied:

a) 0<P(A)<1 and P(S) = 1

b) If A and B are disjoint events that:
- A∩B=0
- P(AUB) = P(A) + P(B)

Question 7

Basic Probability Rules

Answer 7

1 -
-> A and B are two events
-> A is a subset of B
-> B-A = {s ϵ B, s !ϵ A}
-> If B = S then
P(A°) = 1 - P(A)
-> A and B-A are disjoint and
A U (B-A) = B
so by additivity
P(B) = P(A) + P(B-A)

2 -
P(AUB)=P(A)+P(B)-P(A∩B)