Ch.5+6 Probability (Elementary+Discrete)

Question 1

P(A or B) =

Answer 1

P(A) + P(B) - P(A & B)

Question 2

P(A | B) =

Answer 2

Given B has occurred

. P(A & B)
P(A | B) = —————
. P(B)

Question 3

How to judge Event A & B are

1. Independent?
2. Mutually exclusive?

Answer 3

1. Multiplication Rule
   if P(A&B)=P(A)·P(B)
   True⇒ A & B are independent events
2. P(A&B) = 0
   ⇒ Mutually exclusive

Question 4

How to calculate

Probability of the 13th event to be Positive (A)
if the first 12 events are Positive

Answer 4

Frequency of A -12
(Total also -12)

Question 5

Probability can be determined before the fact
∵ Equally Likely Outcomes

Answer 5

Classical Approach
e.g. dice, poker cards

Question 6

Probability based on
Accumulated Historical Data

Answer 6

Empirical Approach
e.g. survey, experiment

Question 7

Probability are determined by
educated guess/ personal belief/ intuition/ expert analysis

Answer 7

Subjective Approach
e.g. stock trend

Question 8

In Discrete Probability Distribution

Mean
&
Variance

Answer 8

Mean μ = E(x)
= ∑ [ P(x)·x ]

Variance σ²
= ∑ [ P(x)·(x-μ)² ]

Question 9

Binomial Probability Formula

Answer 9

P(x) = ₙCₓ · pˣ · qⁿ⁻ˣ

p : probability of A
q : probability of A-bar
n : number of Trials
x : number of A

BINOM.DIST

Question 10

In Binomial Probability Formula

Mean μ
&
Variance σ²

Answer 10

Mean
μ = n·p

Variance
σ² = n·p·q

Question 11

In Poisson Probability Distribution

Mean μ = E(x)
&
Variance σ²

Answer 11

Mean
λ = μ = E(x)
= n·p

Variance
λ = σ²
= n·p·q

Question 12

Poisson Probability Distribution Formula

Answer 12

Poisson

. λˣ·e^(-λ)
P(x) = ————–
. x!

λ : Mean (& Variance)
e: Natural Log (constant)
x: Count of A

Question 13

Prob. Distribution Method
for Question which includes

1. p (%) / n (trials)
2. Time / μ (mean) / x (event)

Answer 13

1. Binomial
2. Poisson