Download Senior Team Mathematics Challenge

Making decisions using
mathematics
Making decisions using mathematics
Making decisions using
mathematics
What are the chances of
choosing the winning set of
numbers for the National
Lottery?
How many possible
combinations of 6 numbers
can be chosen from 49
numbers?
Expected monetary value (EMV)
 An Expected Monetary Value (EMV) calculation is used
to quantify the monetary risk or reward of a particular
outcome.
 EMV = (probability of outcome) x (cost of outcome)
Building project
 Weather
There is a 20% chance of excessive snow which would cause a delay of
approximately 2 weeks which would cost £80,000.
 Construction Materials
There is a 10% probability of the price of construction material dropping, which
will save the project £90,000.
 Workers going on strike
There is a 5% probability of construction coming to a halt if the workers go on
strike. The impact would cause additional costs of £150,000.
 Planning permission
There is a chance of 5% that the planning permission required will be returned
3 weeks earlier than expected, which would create a saving of £115,000.
Decision Trees
decision node
chance node
end node
How to use a decision tree
Kevin has £5000 which he might invest in a new business
scheme.
There is a probability 0.3 of a 5% profit,
probability 0.2 of a 7% profit and a 0.5
probability of a 2.5% loss.
Should Kevin invest his money in this
scheme?
a
How to use a decision tree - solution
Circle indicates
chance
Box indicates
a decision to
be made
£5082.50
0.3
£5250 (profit 5%)
0.2
£5350 (profit 7%)
Invest
£5082.50
0.5
(0.3x£5250)+(0.2x£5350)+(0.5x£4875)
EMV is=£5082.50
£5082.50so
Kevin should invest!
Don’t
invest
Double line to
cross out least
favourable option
£0
Triangle indicates a
final outcome
£4875 (loss 2.5%)
All possible events
that can happen by
chance
Dice Game
In a game you are asked by the Gamekeeper to roll a fair
dice.
If a 5 or a 6 is obtained, the Gamekeeper will pay you £20.
For any other number you have to pay the Gamekeeper
£5.
However, in the second case, instead of paying £5 you can
opt to roll the dice again. If you roll again and score a 6,
the Gamekeeper will pay you £35.
Otherwise you lose a further £5 and so you will need pay
£10 in total.
Dice Game Solution
If decide to play, you might
roll a 5 or 6 , or roll 1-4
First decision is
play or don’t play
Play
1
5 or 6 (p = 3)
- £2.50
£5
2
3
1 – 4 (p = )
£5
Don’t play
For the calculations,
work backwards
£20
A double line goes
on the branch for
Don’t roll
-£5 the least
again
favourable option
1
6 (p = 6)
Roll
- £2.50
again
5
£0
£35
-£10
1-5 (p = 6)
If you roll 1-4, the
decision is then whether to roll again,
in which case you might score a 6 or score 1-5
Risk Analysis…a career
 Well suited to graduates of
mathematics, business,
accountancy or statistics.
 Starting salary of over £21,000
 Salary of between £29,000 and £44,000 after six years
 Risk managers can earn in excess of £70,000
 Opportunities in a range of fields including banking, large
credit organisations, analysing risk of changes in the law,
insurance and many others!
And remember…..
The Further Mathematics
Support Programme
Our aim is to increase the uptake of
AS and A level Further Mathematics
to ensure that more students reach
their potential in mathematics.
The FMSP works closely with
school/college maths departments to
provide professional development
opportunities for teachers and maths
promotion events for students.
To find out more please visit
www.furthermaths.org.uk