8. Probabilities Flashcards
Probability
if I toss a coin I have a 50/ 50 probability it will land on heads
expresses the likelihood of an event happening
Basic ideas
if an event is certain then the probability is 1
if an event is impossible the probability is 0
All probabilities must be between 0 and 1
the higher the probability the more likely it is to happen
In any given scenario, all possibilities must add up to 1
Notation
Probability of event A = P(A)
Complementary rule (something doesn’t happen)
P(NOT A) = 1 - P(A)
Simple probabilities
P(event) = total number of outcomes which constitute the event
/
total possible number of outcomes
Multiplication law
P(A and B both happening)
multiply
Addition law
P( A or B happening)
Simple version of the addition law
Mutually exclusive, cannot both occur and the same time
P(A or B) = P(A) + P(B)
i.e. a particular employee can not simultaneously be aged both over 50 and under 21
Complex version of the addition rule
P(A or B) = P(A) + P(B) - P(A and B)
This is for events that can happen simultaneously NOT MUTUALLY EXCLUSIVE
i.e. an employee could be both over 50 and female
Simple version of the multiplication rule
two events are independent, one event does not affect the probability of the other event occurring
i.e. toss a coin twice
cards, replace the card before the second event
P(A and B) = P(A) x P(B)
Complex version of the multiplication rule
P(A and B) = P(A) x P(B/A)
conditional events - occurrence of one event DOES affect the probability of the other event occurring
i.e. finding the height of an employee is 170cm and is affected if the employee is male or female
Expected values
classing one option as better than another, we choose the option with the highest expected financial return
is a long run average
weighted average
EV = Σ x p(x)
x = units p = probability (f / sum of f)
Payoff tables
expected value tables
Discrete variables
can only consist of certain values i.e no of invoices 1, 2, 3
Continuous variables
can have a value of any level of precision i.e. feet size 10 inches, 10.5 inches, 10.6 inches etc
Discrete variables and probabilities
With discrete variables it is possible to work out the probability of a particular variable occuring
Continuous variables and probabilities
It is not possible to work out the probability of a particular variable occurring. Instead you can use a range of values
e.g. P( height is >1.9m but
Normal distribution
area under the normal curve
area represents the probabilities (must equal one)
area is defined by it’s mean (μ) and it’s standard deviation (σ)
curve is bell shaped and symmetrical
Normal distribution formula
z = x - μ
/
σ
given on the tables
once calculated use tables for the answer
How to solve a normal distribution for the other side
add 0.5 (the other half) to the calculated formula
