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Financial Financial ExpectationExpectationStage 6 - Year 12Stage 6 - Year 12

General Mathematic(HSC)

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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.

Example

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In a coin tossing game you win $1for a head and lose $1for a tail.

F.E. = 12

x $1 +

12

x -$1 = $0

P(H) =12

P(T) = 12

No Gain or Loss per game

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HH

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TT

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Tossing a Coin ExperimentTossing a Coin Experiment

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Financial Expectations

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Financial Expectations

Example: Bet on the RedIn a roulette game you win $1 for a red

and lose $1 for a black and lose $1 for a green.

F.E. = 1837

x $1 +

1837

x -$1 +

= -$0.03

P(R) = 1837

P(B) = 1837

Net Loss of 3 cents per game.

P(G) = 1 37

1 37

x -$1

Red Black Green

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HHHH1122334455667788991010111112121313141415151616171718181919202021212222232324242525

HTHT

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Two-Up - Tossing a Coin ExperimentTwo-Up - Tossing a Coin Experiment

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TTTT

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Financial Expectations

Example: Bet on the Head HeadIn a two-up game you win $1 for a HH

and loose $1 for a TT and loose $1 for a HT.

F.E. = 14

x $1 +

14

x -$1 +

= -$0.50

P(HH) =14

P(TT) = 14

Net Loss of 50 cents per game.

P(HT) = 1 2

1 2

x -$1

HH TT HT