GER1000
Quantitative Reasoning
Chapter: Uncertainty
Unit: Measuring Uncertainty
Assoc Prof Victor Tan
Department of Mathematics
Overview
Random Circumstances
Probability
Relative
Frequency
Personal
probability
Random Circumstances
A random circumstance i

Slide 1 (Intro)
In this last unit of the chapter on Uncertainty, we will continue with the discussion
of the concept of conditional probability.
In particular, we will apply the concept in the circumstances of testing or detecting
rare events which have v

GER1000
Quantitative Reasoning
Chapter: Uncertainty
Unit: Average Values
Assoc Prof Victor Tan
Department of Mathematics
Overview
Insurance
company
Casino
Average Value
Game Show
Option I
Option II
No condition
Answer one MCQ
Correct
$1000
probability 1
$

GER1000
Quantitative Reasoning
Chapter: Uncertainty
Unit: Conditional Probabilities
Assoc Prof Victor Tan
Department of Mathematics
Overview
Conditional Probability
P(event A occurs, given that event B has occurred)
dependent or independent
Drawing a Card

GER1000
Quantitative Reasoning
Chapter: Uncertainty
Unit: P-Values
Assoc Prof Victor Tan
Department of Mathematics
Overview
P-values
Coin Tossing
Hypothesis Test
Statistically
Significant
New Drug Testing
Coin Tossing
Is the coin not fair?
1st toss
2nd to

GER1000
Quantitative Reasoning
Chapter: Uncertainty
Unit: Simple Probability Rules
Assoc Prof Victor Tan
Department of Mathematics
Overview
Complement
rule
Addition
rule
Multiplication
rule
Mutually exclusive events
Independent
events
Events
Rolling a fai

Slide 1 (Intro)
Suppose you have taken the mid-term test of a module and received an A grade.
Based on this information, you want to know the chance for you to get an A grade
for the final. In this scenario, getting an A grade for final is uncertain, whil

Slide 1 (Intro)
In this unit, we will discuss the concept of average values, which is also known as
expected value or mean value in statistics.
For certain random circumstances, every outcome may be associated with a
numerical value. Consequently, when we

Slide 1 (Intro)
In this unit, we shall introduce the concept of p-value. This is a probability arising
from hypothesis testing, which is a procedure based on how likely it would be for a
set of observations to occur if we assume certain hypothesis is true

Slide 1 (Intro)
In the first unit of this chapter, we talk about the probability of outcomes of random
circumstances, which are values between 0 and 1.
In this unit, we are going to see how simple outcomes can be put together to form
some complex events,

Slide 1 (Intro)
Hi there, my name is Victor Tan.
In this new chapter, we are going to talk about Uncertainty.
We face with uncertainty every day.
For example: Will it rain today? Will the bus arrive on time? Will the MRT train
break down?
Sometimes we wan

GER1000
Quantitative Reasoning
Chapter: Uncertainty
Unit: Testing Rare Events
Assoc Prof Victor Tan
Department of Mathematics
Overview
Medical
Screening
QR
Framework
Conditional
Probabilities
Medical Screening
Rare disease
tested
positive
having the
disea