Module 3 - Section 1

Question 1

Random Phenomenon

Answer 1

considered a random phenomenon if we know what outcomes could happen, but we do not knw which particular outcome did or will happen
ex: coin toss, covid numbers

Question 2

Probability Theory

Answer 2

probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

Question 3

trial

Answer 3

each occasion upon which we observe a random phenomena

can be one coin toss or two if they are done together

Question 4

outcome

Answer 4

after a trial, the result or value is the outcome

ex: 2 coin tosses: HT

Question 5

sample space

Answer 5

the collection of all possible outcomes

Question 6

event

Answer 6

combination of outcomes or a subset of the sample space
ex: event that dice rolled is even
A= or B =
the probability of an event is written as P(A) or P(B)

Question 7

Venn diagram

Answer 7

a picture that depicts all the possible outcomes of an experiment
The outer box represents the sample space, and the appropriate events are circled and labelled
ex: box with numbers 1-6 written and 2,4,6 circled and labelled as the event that an even number is rolled

Question 8

Tree diagram

Answer 8

visualize sample spaces with a small number of outcomes
each outcome on the tree diagram is represented by a branch of the tree
H ——–H
…-——-T
T———-H
…-——-T

Question 9

probability

Answer 9

the probability of any outcome (or event) of a random phenomena is the proportion of times the outcome would occur in a very long series of repetitions (probability is the measure for the likelihood or chance of a future event)
always a nuber from 0-1

Question 10

Law of Large Numbers (LLN)

Answer 10

the long run relative frequency of repeated events gets closer and closer to a single value
says nothing about the short-run behaviour
the relative frequency will only even out in the very very longggg run

Question 11

equally likely probability

Answer 11

when the probability of all outcomes are equal

ex: fair die, unbiased coin

Question 12

Total Probability Rule

Answer 12

The probability of the set of all possible outcomes of a trial must be 1

Question 13

Compliment Rule

Answer 13

P(A) + P(Ac) = 1

P(Ac) = 1 - P(A)

Question 14

Disjoint

Answer 14

or Mutually Exclusive

no common outcomes