Tutorial 4 : Uncertainty

1. Probability rules:

- Complement rule
P(A) = 1-P(not A)

- Addition rule
P(A happen or B happen)  = P(A) + P(B) - P(A&B)
Not mutually exclusive = P(A) + P(B)
we need to take away the repeated

- Multiplication Rule
P(A and B) = P(A) * P(B|A) {Knowing that A has happened}
= P(B) * P(A|B)

If there's an association, they are dependent

- "At least One" rule
P(at least one) = 1- p(none)

2. Average Value
AV = p(loosing ) * -ve amt for loosing + p(winning)*(+ve amt for winning)
It makes sense for us to play the game because the average value for the player to win.
Casino:
All the avg values are negative

3. Hypothesis testing (Exam point)
- Is our observation by chance.
P - value is the addition of 3 prob
- observation
- Equally extreme than observation
- More extreme than observation
Null Hypo: nothing is going on and the thing we observe is by chance
If P-value is smaller than the level of significance, the observation does not happen by chance.
(Reject Null Hypothesis)
A large P-value doesn't mean it happen by chance but we don't have enough evidence to claim that it doesn't happen by chance

4. Rare events
- Base rate
p(disease) = 0.001
Sensitive of test
p(pos | dis)  = I got tested positive and have the disease
Specificity test
P(neg | no dis) = I got test negative and actually don't have the disease

Table:
Row: Test pos | test neg | row sum
Col: have dis | do not have dis | col sum

Notes