The probability of an event not happening - five friends play mini golf

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Xiaodan Leng 5 years, 8 months ago

Created this as a copy of The probability of an event not happening - five friends play mini golf.

Name	Status	Author	Last Modified
The probability of an event not happening - five friends play mini golf	Ready to use	Elliott Fletcher	19/12/2022 12:28
Probability of scoring at basketball given probability of not scoring	Ready to use	Christian Lawson-Perfect	20/11/2019 14:41
Hugh's copy of The probability of an event not happening - five friends play mini golf	draft	Hugh O'Donnell	16/01/2018 13:48
Simon's copy of The probability of an event not happening - five friends play mini golf	draft	Simon Thomas	08/05/2019 09:46
Maria's copy of Probability of scoring at basketball given probability of not scoring	draft	Maria Aneiros	27/05/2019 02:29
The probability of an event not happening - five friends play mini golf	draft	Xiaodan Leng	11/07/2019 02:02
Probability of scoring at basketball given probability of not scoring	draft	Xiaodan Leng	11/07/2019 02:03

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Question statement

Five friends are playing a game of mini-golf.

The probability that each person wins the game, $\mathrm{P}(\text{Person})$ , is given in the table.

Person	{people[0]['name']}	{people[1]['name']}	{people[2]['name']}	{people[3]['name']}	{people[4]['name']}
$\mathrm{P}(\text{Person})$	$\var{probs[0]}$	$\var{probs[1]}$		$\var{probs[2]}$	$\var{probs[3]}$

Give any introductory information the student needs.

			Name	Type	Generated Value

people	list	List of 5 items
raw_probs	list	List of 5 items
probs	list	[ 0.13, 0.32, 0.28, 0.12 ]
person	dict	Dictionary with 3 entries
name	string	Ismaeel

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random_people(5)

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: `list`

[ [ "gender": safe("female"), "name": safe("Aila"), "pronouns": [ "they": safe("she"), "their": safe("her"), "theirs": safe("hers"), "them": safe("her"), "themself": safe("herself") ] ], [ "gender": safe("male"), "name": safe("Justin"), "pronouns": [ "they": safe("he"), "their": safe("his"), "theirs": safe("his"), "them": safe("him"), "themself": safe("himself") ] ], [ "gender": safe("male"), "name": safe("Ismaeel"), "pronouns": [ "they": safe("he"), "their": safe("his"), "theirs": safe("his"), "them": safe("him"), "themself": safe("himself") ] ], [ "gender": safe("male"), "name": safe("Albie"), "pronouns": [ "they": safe("he"), "their": safe("his"), "theirs": safe("his"), "them": safe("him"), "themself": safe("himself") ] ], [ "gender": safe("female"), "name": safe("Ella-Rose"), "pronouns": [ "they": safe("she"), "their": safe("her"), "theirs": safe("hers"), "them": safe("her"), "themself": safe("herself") ] ] ]

→ Used by:

person

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

What is $\mathrm{P}(\text{not } \var{name})$?

Unnamed gap

Advice

All probability situations can be reduced to two possible outcomes: success or failure.

When we express the outcomes in this way we say that they are complementary.

The sum of the probability of an event and its complement is always $1$.

If $\mathrm{P}(\mathrm{E})$ is the probability of an event $\mathrm{E}$ happening and $\mathrm{P}(\bar{\mathrm{E}})$ is the probability of that event not happening then

\[\mathrm{P}(\mathrm{E}) +\mathrm{P}(\bar{\mathrm{E}}) = 1.\]

Rearranging this equation gives:

\[\mathrm{P}(\bar{\mathrm{E}}) = 1 - \mathrm{P}(\mathrm{E})\]

We can think of this game as having two possible outcomes: either Dexter wins or Dexter doesn't win.

This means that

\[\mathrm{P}(\var{name}) + \mathrm{P}(\text{not } \var{name}) = 1 \text{.}\]

a)

If {name} doesn't win the game then that means that one of the other four players must win the game.

So the probability of {name} not winning the game is the same as the probability of any of the other four players winning the game.

Therefore

\begin{align}
\mathrm{P}(\text{not }\var{name}) &= \mathrm{P}(\var{people[0]['name']})+\mathrm{P}(\var{people[1]['name']})+\mathrm{P}(\var{people[1]['name']})+\mathrm{P}(\var{people[1]['name']}) \\
&= \var{latex(join(probs,' + '))}\\
&= \var{sum(probs)}.
\end{align}

b)

Rearranging the equation above gives

\[\mathrm{P}(\var{name}) = 1 - \mathrm{P}(\text{not } \var{name}).\]

We know from a) that $\mathrm{P}(\text{not } \var{name}) = \var{sum(probs)}$.

Therefore

\begin{align}
\mathrm{P}(\var{name}) &= 1 - \mathrm{P}(\text{not } \var{name})\\
&= 1 - \var{sum(probs)}\\
&= \var{1-sum(probs)}.
\end{align}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
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Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
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This question is used in the following exam:

testert by cormac murphy in cormac's workspace.

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The probability of an event not happening - five friends play mini golf

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

Loading...

Error

The probability of an event not happening - five friends play mini golf

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

Generated value: `list`