8. Probabilities

Question 1

Probability

Answer 1

if I toss a coin I have a 50/ 50 probability it will land on heads

expresses the likelihood of an event happening

Question 2

Basic ideas

Answer 2

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

Question 3

Notation

Answer 3

Probability of event A = P(A)

Question 4

Complementary rule (something doesn’t happen)

Answer 4

P(NOT A) = 1 - P(A)

Question 5

Simple probabilities

Answer 5

P(event) = total number of outcomes which constitute the event
/
total possible number of outcomes

Question 6

Multiplication law

Answer 6

P(A and B both happening)

multiply

Question 7

Addition law

Answer 7

P( A or B happening)

Question 8

Simple version of the addition law

Answer 8

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

Question 9

Complex version of the addition rule

Answer 9

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

Question 10

Simple version of the multiplication rule

Answer 10

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)

Question 11

Complex version of the multiplication rule

Answer 11

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

Question 12

Expected values

Answer 12

classing one option as better than another, we choose the option with the highest expected financial return

is a long run average

Question 13

weighted average

Answer 13

EV = Σ x p(x)

x = units
p = probability (f / sum of f)

Question 14

Payoff tables

Answer 14

expected value tables

Question 15

Discrete variables

Answer 15

can only consist of certain values i.e no of invoices 1, 2, 3

Question 16

Continuous variables

Answer 16

can have a value of any level of precision i.e. feet size 10 inches, 10.5 inches, 10.6 inches etc

Question 17

Discrete variables and probabilities

Answer 17

With discrete variables it is possible to work out the probability of a particular variable occuring

Question 18

Continuous variables and probabilities

Answer 18

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

Question 19

Normal distribution

Answer 19

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

Question 20

Normal distribution formula

Answer 20

z = x - μ
/
σ

given on the tables

once calculated use tables for the answer

Question 21

How to solve a normal distribution for the other side

Answer 21

add 0.5 (the other half) to the calculated formula