General Mathematic
(HSC)
Financial
Expectation
Stage 6 - Year 12
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1
Financial Expectations
is the average financial return from a
chance situation.
It tells us if we can expect a gain or a loss
over a long period of time.
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Example
In a coin tossing game you win $1
for a head and lose $1for a tail.
P(H) = 1
P(T) = 1
2
2
F.E. = 1 x $1 + 1 x -$1 = $0
2
2
No Gain or Loss per game
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Tossing a Coin Experiment
H
T
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Financial Expectations
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4
Financial Expectations
Example: Bet on the Red
In a roulette game you win $1 for a red and
lose $1 for a black and lose $1 for a green.
P(R) = 18
37
P(B) = 18
37
P(G) = 1
37
18
F.E. =
x $1 + 18 x -$1 + 1 x -$1 = -$0.03
37
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Red
Black
Green
Net Loss of 3 cents per game.
Two-Up - Tossing a Coin Experiment
H
H
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HT
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T
T
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6
Financial Expectations
Example: Bet on the Head Head
In a two-up game you win $1 for a HH and
loose $1 for a TT and loose $1 for a HT.
P(HH) = 1
4
P(TT) = 1
4
P(HT) = 1
2
1
F.E. =
x $1 + 1 x -$1 + 1 x -$1 = -$0.50
4
4
2
HH
TT
HT
Net Loss of 50 cents per game.