Probability: Conditional Probability 3 - without Venn

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Ruth Hand

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Ready to use

3 years, 8 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

Published this.

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Ruth Hand 3 years, 8 months ago

Gave some feedback: Ready to use

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Ruth Hand 3 years, 8 months ago

Created this as a copy of Probability: Conditional probability 2 - with Venn.

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

Give any introductory information the student needs.

			Name	Type	Generated Value

A	number	0.72
B	number	0.87
justA	number	0.08
justB	number	0.23
both	number	0.64
AuB	number	0.95
neither	number	0.05
sol	number	0.7356321839
sol2	number	0.74

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

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

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Generated value: `number`

0.72

This variable doesn't seem to be used anywhere.

Advice

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

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

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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Probability: Conditional Probability 3 - without Venn

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 8 months ago

Ruth Hand 3 years, 8 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Number entry

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Probability: Conditional Probability 3 - without Venn

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 8 months ago

Ruth Hand 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

Generated value: `number`