Link Probabilities

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Question statement

Some short network links are given below, made up of components (a), (b), and (c). The components work independently, so if one fails the others are not affected.

The probability of each component being functional is:

Component (a): $P(A) = \var{probA}$ ;
Component (b): $P(B) = \var{probB}$ ;
Component (c): $P(C) = \var{probC}$ .

In each part, give all decimal places that you have calculated.

Give any introductory information the student needs.

			Name	Type	Generated Value

probA	number	0.9
probB	number	0.8
probC	number	0.6
series	number	0.72
parallel	number	0.98
combined	number	0.588

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random([0.5,0.6,0.7,0.8,0.9])

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: `number`

0.9

This variable doesn't seem to be used anywhere.

Advice

Series:

The probability that the link works is $P(A \wedge B) = P(A) \times P(B) = \var{probA} \times \var{probB} = \simplify{{probA}*{probB}}$ .

Parallel:

The probability that the link works is $P(A \vee B) = P(A) + P(B) - P(A) \times P(B) = \var{probA} + \var{probB} - \var{probA} \times \var{probB} = \simplify{{probA} + {probB} - {probA}*{probB}}$ .

Combined:

The probability that the link works is $P((A \vee B) \wedge C) = P(A \vee B) \times P(C) = \simplify{{probA} + {probB} - {probA}*{probB}} \times \var{probC} = \simplify{({probA} + {probB} - {probA}*{probB})*{probC}}$ .

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This question is used in the following exam:

Maths and Cryptography Exam Practice by Alexander Corner in Intro Cryptography.

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Taxonomy: mathcentre

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Alexander Corner 3 months ago

Alexander Corner 3 months ago

Alexander Corner 3 months ago

Error in variable testing condition

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Generated value: `number`

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Number entry

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Link Probabilities

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Alexander Corner 3 months ago

Alexander Corner 3 months ago

Alexander Corner 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

Generated value: `number`