Probability: Conditional Probability 1

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Ruth Hand

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2 years, 9 months ago

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Christian Lawson-Perfect 2 years, 7 months ago

Published this.

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Ruth Hand 2 years, 9 months ago

Gave some feedback: Ready to use

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Ruth Hand 4 years, 7 months ago

Created this as a copy of Probability: from a Venn diagram.

Name	Status	Author	Last Modified
Probability: from a Venn diagram	Ready to use	Ruth Hand	16/01/2023 13:40
Probability: Conditional Probability 1	Ready to use	Ruth Hand	16/01/2023 14:35
Sets: Venn diagram	Ready to use	Ruth Hand	16/01/2023 13:14
Probability: Conditional probability 2 - with Venn	Ready to use	Ruth Hand	16/01/2023 14:22
Sets: Set logic	Ready to use	Ruth Hand	16/01/2023 13:24
Sets: set inequality	Ready to use	Ruth Hand	16/01/2023 13:25
Sets: Set notation	Ready to use	Ruth Hand	16/01/2023 13:25
Probability: Conditional Probability 3 - without Venn	Ready to use	Ruth Hand	16/01/2023 14:20

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Question statement

{geogebra_applet('https://www.geogebra.org/m/rudd6jns',[a:{neither}, b:{A}, c:{both},d:{B}])}

Give any introductory information the student needs.

			Name	Type	Generated Value

A	number	0.71
B	number	0.42
justA	number	0.58
justB	number	0.29
both	number	0.13
AuB	number	1
neither	number	0
sol	number	0.3095238095
sol2	number	0.31

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Generated value: `number`

0.71

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{geogebra_applet('https://www.geogebra.org/m/rudd6jns',[a:{neither}, b:{A}, c:{both},d:{B}])}

$P(A \vert B)$ can be read as "the probability of $A$ given $B$", or "if we know $B$ is true, what is the probability of $A$?".

We can use the formula, or the Venn diagram; the Venn diagram clarifies the standard formula:

$P(A \vert B) = \frac{P(A \cap B)}{P(B)}$

since we know $B$ is true, we restrict ourselves to the domain of $B$, and then look for where $A$ is true, which now is only the intersection, $A \cap B$.

$P(A \vert B) = \frac{P(A \cap B)}{P(B)} = \frac{\var{both}}{\var{B}} = \var{precround(both/B,2)}$.

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This question is used in the following exams:

Example exam by Ben Parker in Ben's workspace.
Week 8 Probability II by Peter Chapman in Peter's workspace.
Probability Practice by Rabail Tahir in Rabail's workspace.
Probability by Chris Templet in Chris's workspace.
Maths 3 Conditional Probability participation quiz by Aoife O'Brien in Aoife's workspace.
Mathematics 3 Probability Learning Quiz by Aoife O'Brien in Aoife's workspace.

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Taxonomy: Context

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Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 2 years, 9 months ago

Ruth Hand 4 years, 7 months ago

Error in variable testing condition

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Generated value: `number`

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Probability: Conditional Probability 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 2 years, 9 months ago

Ruth Hand 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `number`