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Question 1

what is probability?

Answer 1

probability deals with predicting the likelihood of future events

Question 2

what is statistics?

Answer 2

statistics involves the analysis of the frequency of past events

Question 3

what is an experiment?

Answer 3

any procedure that can be repeated any number of times and has a
well-defined set of potential Outcomes

Question 4

what is an outcome?

Answer 4

𝜔, is a potential eventuality of an Experiment.

Question 5

what is the sample space

Answer 5

or ‘universe’: Ω, the set of all possible outcomes (𝜔) of the
experiment.
o An outcome is a member of the sample space, so we can write 𝜔 ∈ Ω.

Question 6

what is an event

Answer 6

𝐴, is some subset of Ω, 𝐴 ⊆ Ω. Can be a single outcome.

Question 7

what are the events for a dice

Answer 7

The sample space for a dice roll contains six outcome

Question 8

what is the sample space for a dice

Answer 8

Ωdice = {1, 2, 3, 4, 5, 6}.

Question 9

what are the outcomes for a dice?

Answer 9

Outcomes, 𝜔 = {1}, or 𝜔 = {5}, or any other integer number between 1 and 6

Question 10

We can describe three Events 𝐴, 𝐵 and 𝐶 as follows:
o Event 𝐴 - the rolled number is equal to 6;
o Event 𝐵 - the rolled number is odd;
o Event 𝐶 - the rolled number is greater than 3;

what are the outcomes?

Answer 10

Each of these events would then correspond to one or more outcomes in Ωdice, namely:
o 𝐴 = {6} 𝐵 = {1, 3, 5} 𝐶 = {4, 5, 6}

Question 11

what is the union of A and B

Answer 11

The union of 𝐴 and 𝐵, denoted 𝐴 ∪ 𝐵, is the set of those outcomes which belong to
𝐴 or 𝐵 (or both).
o 𝐴 ∪ 𝐵 occurs if 𝐴 occurs or 𝐵 occurs (or they both occur)

Question 12

what is the intersection of A and B

Answer 12

The intersection of 𝐴 and 𝐵, denoted 𝐴 ∩ 𝐵, is the set of those outcomes which
belong to both 𝐴 and 𝐵.
o 𝐴 ∩ 𝐵 occurs if 𝐴 occurs and 𝐵 occurs.

Question 13

what is the complement of A

Answer 13

The complement of 𝐴, denoted 𝐴, is the set of those outcomes which do not belong
to 𝐴.
o 𝐴 occurs if 𝐴 does not occur

Question 14

what is the difference between set theory and probability theory when it comes to intersection notation

Answer 14

the intersection of
two sets. (𝐴 ∩ 𝐵) is used by the set theory community. However, in the context of
probability theory, this is more commonly represented as (𝐴, 𝐵).

Question 15

what is the 1st axiom of probability

Answer 15

𝑃 𝐴 ∈ ℝ
0 ≤ 𝑃 𝐴 ≤ 1
The probability of an event A is a real number
between 0 and 1.

Question 16

what is the 2nd axiom of probability

Answer 16

𝑃 Ω = 1 The certain event has
probability 1

Question 17

what is the 3rd axiom of probability

Answer 17

If A ∩ 𝐵 = ∅
Then 𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃(𝐵)
and
1𝑖=ڂ ��
𝑛 𝐴𝑖 = σ𝑖=1
𝑛 𝑃(𝐴𝑖)
The probability of the union of disjoint events is
equal to the sum of their probabilities.

Question 18

what is the The Inclusion-Exclusion Formula

Answer 18

𝑃 𝐴 ∪ 𝐵 = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴, 𝐵)

Question 19

what is conditional probability

Answer 19

Let 𝐴 and 𝐵 be events with 𝑃(𝐵) > 0. The conditional probability 𝑃(𝐴|𝐵)
(probability of 𝐴 given 𝐵) is defined as:
𝑃(𝐴|𝐵) =𝑃(𝐴,𝐵)/ 𝑃(𝐵)
* This represents the probability that 𝐴 will occur given that 𝐵 has occurred