15 - Risk and probability

Question 1

what is risk vs uncertainty

Answer 1

RISK = several possible future outcomes usually due to past experience

UNCERTAINTY = future is unknown, decision maker has no past experience on which to base predictions

Question 2

what is probability

Answer 2

the likelihood of a particular outcome from a given event

Question 3

what are the types of probability

Answer 3

EXACT = applies to a population eg drawing red ball out of a bag
EMPIRICAL = derived from historical observations eg probability of no of customers visiting a shop
SUBJECTIVE = based on judgement eg chance of finding a diamond

Question 4

probability of an outcome formula

Answer 4

no of ways in which x can occur / total no of possible outcomes

Question 5

what is a mutually exclusive outcome

Answer 5

OR outcome

outcome of one event cant happen at the same time as the outcome of another

Question 6

non mutually exclusive outcome

Answer 6

OR outcome

both outcomes can occur at the same time

eg student studying CIMA and country of birth is the UK

Question 7

independent events

Answer 7

AND events

one outcome has nothing to do with another

eg, asking two unrelated students where they were born

Question 8

dependent events

Answer 8

AND events

one outcome depends upon something else taking place either with a proviso regarding the first event or given it has happened

eg asking twins where they were born (successive events)

Question 9

independent events laws and formula

Answer 9

MULTIPLICATION LAW - AND

p (x and y) = p(x) x p(y)

eg probability of getting two heads in two throws of a coin

Question 10

dependent events laws and formula

Answer 10

MULTIPLICATION LAW - AND

p (x and y) = p(x)x p (y/x)
( / = given that x has already happened)

eg,
16/30 x 15/29
for chance of male student walking into classroom, take away the one who first walks in on the second probability

Question 11

mutually exclusive outcomes formula

Answer 11

ADDITION LAWS - OR

p (x or y) = p(x) + p(y)

Question 12

non mutually exclusive outcomes

Answer 12

ADDITION LAWS - OR

p (x or y) = p (x) + p (y) - p (x and y)

eg, probability of a bday in may (x) or on a sunday (y)

x = 1/12
y = 48/336 or 1/7 (48 weeks out of 336 days)

= 1/12 + 1/7 - (1/12 x 1/7) = 3/14

Question 13

what is a complementary probability

Answer 13

when an event is repeated successively so we split between success and failure

Question 14

complementary probability formula

Answer 14

P (success) = 1 - P (failure)

eg, coin tossed 4 times, probability of getting at least one head

P (no heads) = 1/2 x 1/2 x 1/2 x 1/2 = 1/16

P (1 head) = 1 - P (no heads)
= 1 - P (1/16) = 15/16

Question 15

what is conditional probability

Answer 15

chance of an event occurring given other events have already taken place

(usually given figures which can be used to make a table with figures down and across which you can cross reference)

Question 16

how to find a probability from a contingency table (conditional probability)

Answer 16

eg,
P (used normal shampoo / shows no improvement)
= no of people using normal shampoo with no improvement / total no of people showing no improvement

OR

P (shows improvement / used new shampoo)
= no of people using new shampoo with improvement / no of people using new shampoo

Question 17

what is expected values

Answer 17

= average outcome

when final outcome is unknown and range of possible outcomes quantified, probabilities can be assigned to these outcomes

Question 18

EV formula

Answer 18

= sum of probability x outcome

eg
(2/3 x 13500) + (1/3 x 6500) = 11167

Question 19

how can a decision tree be evaluated

Answer 19

calculate expected values at outcome points and take highest benefit at these points

Question 20

what is a payoff table used for

Answer 20

to consider outcome of each choice against an uncontrollable event

Question 21

what is a decision variable

Answer 21

different options a manager has to choose between

Question 22

what is in a payoff table

Answer 22

variable subject to uncertainty against the decision variable

Question 23

limitations of an expected value

Answer 23

• is a long term average, unsuitable for one off decisions
• results dependent on accuracy of probability distribution
• takes no account of the risk
• may not represent a single possible outcome

Question 24

what is a joint probability table

Answer 24

records the range of possible outcomes where there are two variables that are uncertain or risky