Identify independent events

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Christian Lawson-Perfect	said	Should not be used	7 years, 7 months ago
Elliott Fletcher	said	Needs to be tested	7 years, 8 months ago
Chris Graham	said	Has some problems	7 years, 8 months ago

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Christian Lawson-Perfect 7 years, 7 months ago

Gave some feedback: Should not be used

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Christian Lawson-Perfect 7 years, 7 months ago

Saved a checkpoint:

The options don't explicitly list two events! They're all of the form "event A given event B" - B isn't an event you can put a probability on, because it's already happened.

I can't find a quick way of rewording this so it makes sense, so I'm marking as shouldn't use.

Restore this checkpoint

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Elliott Fletcher commented 7 years, 8 months ago

Thanks for the feedback Chris, i have tried a new way of formatting the advice for part b), so hopefully it looks better now. Also i have tried to draw my conclusions earlier in b) as well, i just left it as it was for the die one as i thought there wasn't much more i could do for that one.

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham 7 years, 8 months ago

Gave some feedback: Has some problems

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Chris Graham commented 7 years, 8 months ago

This looks good now. Just a couple of small changes to the advice:

It doesn't make sense to number the parts of the advice in b), since they are not numbered in the question. Either number them (i),(ii),(iii), or find a different way to format the advice for b).

The student does not need to work out the probabilities in order to answer the question, which is assessing their understanding of the concept. I would prefer that you draw your conclusion earlier in the advice for each part (e.g. for the cards, at the point where you state there are now only 51 cards in the deck, and only 3 kings) And then go on after that, with something like. "In fact, we can calculate...".

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Elliott Fletcher commented 7 years, 8 months ago

Thanks for the feedback Chris, i've reworded the statements a bit hopefully they will be clearer now.

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 8 months ago

I'm not sure there's any reason to have "Must the fraction be reduced" ticked. I can't think of a reason why the student might enter any other equivalent fraction. I would untick to remove the prompt, which could unnecessarily confuse a student.

The following statement,

"Randomly selecting a boy from a class of 15 boys and 15 girls given that the previous randomly selected student from the class was a girl"

is ambiguous and needs to be worded differently. Has the girl been removed from the class? Without that information, it is impossible to answer.

To some extent, the same is true of the card deck question, which could also be clearer.

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Chris Graham 7 years, 8 months ago

Gave some feedback: Has some problems

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher 7 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Identify independent events	Should not be used	Elliott Fletcher	20/11/2019 14:40
The gambler's fallacy - probability of getting heads again after repeatedly getting heads	Ready to use	Christian Lawson-Perfect	20/11/2019 14:43
Maria's copy of The gambler's fallacy - probability of getting heads again after repeatedly getting heads	draft	Maria Aneiros	27/05/2019 02:29
The gambler's fallacy - probability of getting heads again after repeatedly getting heads	draft	Xiaodan Leng	11/07/2019 02:00
SA15 Intuitive Probability	Ready to use	Upuli Wickramaarachchi	04/04/2024 11:33

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

no_flips

integer

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(6..9)

JME function reference

Description

Number of flips of the coin

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

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Choose several from a list

Choose several from a list

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

Which of the following are examples of independent events?

Minimum marks

Maximum marks

Show correct answer on reveal?

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Advanced settings

Number of display columns

(not displayed in columns)

Minimum answers

Maximum answers

What to do if wrong number of answers selected:

Custom marking matrix?

Show choice feedback state?

Marking method

For each choice, specify the number of marks to add or subtract when the student picks it.

Variable list of choices?

Shuffle order of choices?

Rolling a $4$ on a die given that the previous $5$ rolls have all landed on a $6$ .

Marks: Distractor Message:
Randomly removing a king card from a standard deck of cards given that one king card has already been removed from the deck.

Marks: Distractor Message:
Randomly removing a boy from a class that initially consisted of $15$ boys and $15$ girls given that the previous randomly removed student from the class was a girl.

Marks: Distractor Message:

Advice

Rolling a 4 on a die given that the previous 5 rolls have all landed on a 6.

Each roll of a die is independent from all previous rolls - the outcome of one roll does not change the likelihood of getting any particular score on the next roll.

Therefore these events are independent.

Randomly removing a King card from a standard deck of cards given that one card has already been removed from the deck.

The probability of removing a King from the deck depends on whether the first card removed was also a King.

If the first card was a King, then only three Kings are left. If it wasn't a King, then there are still four Kings in the deck.

So the probability of picking a King is not independent of the previous card removed.

Randomly removing a boy from a class that initially consisted of 15 boys and 15 girls given that the previous randomly removed student from the class was a girl.

We are told that the class consists of $15$ boys and $15$ girls.

So the probability that a randomly removed student from the class is a boy is initially

$\displaystyle\frac{15}{30} = \displaystyle\frac{1}{2}.$

If we randomly withdraw one student from the class and this student is a girl, then this means that there are now $15$ boys and $14$ girls in the class.

As there are now fewer students in the class, the probability of randomly removing a boy from the class will change, meaning that these events are not independent.

In fact, if we now randomly withdraw another student from the class, the probability that this student is a boy is now $\displaystyle\frac{15}{29}$ .

Hence the fact that the first randomly removed student is a girl causes the probability of the next randomly removed student being a boy to increase.

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This question is used in the following exams:

Probability by Elliott Fletcher in Elliott's workspace.
Probability by Elliott Fletcher in Elliott's workspace.
Transition Probability by Chris Templet in Chris's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

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Identify independent events

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Choose several from a list

Advanced settings

Generated value: `integer`