Convert gambling odds to probabilities, ,

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

The following odds are given for {event} {between} {player1} and {player2}

{player1}

$\var{odds11}: \var{odds12}$ on

{player2}

$\var{odds21}: \var{odds22}$ against

Convert these statements about odds into probabilities.

Give your answers as fractions.

Give any introductory information the student needs.

			Name	Type	Generated Value

odds12	decimal	dec("7")
odds11	integer	8
den2	decimal	dec("28")
den1	decimal	dec("15")
wdw	string	A bookmaker lists
player2	string	England
player1	string	Australia
t	integer	4
between	string	between
odds22	decimal	dec("11")
event	string	the next series of games
odds21	integer	17

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
round((t*round(odds11+1)/2+(20-t)*(odds11-1))/20)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `decimal`

dec("7")

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
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Part b) Gap-fill
1. Gap Mathematical expression
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Gap-fill

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You should take the bet if you think that $\Pr(\var{player1}\text{ win})$ is greater than Unnamed gap

Advice

a)

Odds of $\var{odds11}: \var{odds12}$ on means that you should take the bet if you think the probability of {player1} winning is greater than:

$\frac{\var{odds11}}{\var{odds11}+\var{odds12}} = \simplify[std]{{odds11}/{odds11+odds12}}$

b)

Odds of $\var{odds21}: \var{odds22}$ against means that you should take the bet if you think that the probability of {player2} losing is less than:

$\frac{\var{odds21}}{\var{odds21}+\var{odds22}} = \simplify[std]{{odds21}/{odds21+odds22}}$

That is, if you think the probability of {player2} winning is greater than:

$1- \simplify[std]{{odds21}/{odds21+odds22}}=\simplify[std]{{odds22}/{odds21+odds22}}$

Note that the sum of these probabilities is:

$\simplify[std]{{odds11}/{odds11+odds12}}+\simplify[std]{{odds22}/{odds21+odds22}}=\simplify[std]{{odds11*odds21+odds22*odds12+2*odds11*odds22}/{odds11*odds21+odds22*odds12+odds11*odds22+odds12*odds21}}$

which is less than $1$ , as otherwise you could bet on both to win and not lose any money!

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Taxonomy: mathcentre

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Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: `decimal`

Parts

Gap-fill

a)

b)

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Convert gambling odds to probabilities, ,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: decimal

Parts

Gap-fill

a)

b)

Generated value: `decimal`