probability complement rule

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From users who are members of MASH Bath: Question Bank :

Ben McGovern

said

Ready to use

2 years, 9 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

Published this.

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Ben McGovern 2 years, 9 months ago

Gave some feedback: Ready to use

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Ruth Hand 4 years, 3 months ago

Created this.

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Question statement

Two $\var{n}$ -sided dice, each with sides labelled $1,2...\var{n}$ are rolled and their scores are added.

Give any introductory information the student needs.

			Name	Type	Generated Value

min	list	[ 2, 3, 4 ]
options	list	[ 1, 3, 6 ]
choice	integer	0
total	integer	81
n	integer	9
pairs	list	Nested 6×2 list
pairschoice	list	[ 0, 2, 5 ]
pairstruncate	list	[ [ 1, 1 ] ]
event	string	event
isorare	string	is

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
list(2..4)

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`

[ 2, 3, 4 ]

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 the probability that the score is less than or equal to $\var{min[choice]}$ ?

Unnamed gap (Give your answer as a fraction)

Advice

part a)

We are looking for pairs of numbers than total to make $\var{min[choice]}$ or less, which is quite a small total, so it doesn't take too long to find that the pairs of numbers are:

$\var{pairstruncate}$

so there {isorare} $\var{pairschoice[choice]+1}$ {event} we are interested in, and therefore the probability is

$P(\text{total is} \leq \var{min[choice]}) = \frac{\var{pairschoice[choice]+1}}{\var{total}}$

part b)

There are a very large number of ways to totals of $\var{min[choice]+1}$ or greater, so in this case we use the complement rule;

$P(A') = 1-P(A)$

which in this case means

$P(\text{total is}\ge \var{min[choice]+1}) = 1-P(\text{total is} \leq \var{min[choice]}) = 1-\frac{\var{pairschoice[choice]+1}}{\var{total}} = \var[fractionnumbers]{1-options[choice]/{total}}$

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Number entry
Number entry		Hasn't run yet
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 2 years, 9 months ago

Ruth Hand 4 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

part a)

part b)

Loading...

Error

probability complement rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 2 years, 9 months ago

Ruth Hand 4 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

part a)

part b)

Generated value: `list`