Roll a pair of dice - find probability at least one die shows a given number, , ,

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Nigel Atkins

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Nigel Atkins 8 years ago

Created this as a copy of Roll a pair of dice - find probability at least one die shows a given number..

Name	Status	Author	Last Modified
Roll a pair of dice - find probability at least one die shows a given number.	Ready to use	Newcastle University Mathematics and Statistics	04/04/2023 08:39
Roll a pair of dice - find probability at least one die shows a given number, , ,	draft	Nigel Atkins	01/03/2017 13:39
Roll a pair of dice - find probability at least one die shows a given number.	Ready to use	Xiaodan Leng	02/11/2019 21:05
Blathnaid's copy of Roll a pair of dice - find probability at least one die shows a given number.	draft	Blathnaid Sheridan	23/08/2019 17:51

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Question statement

Two fair six-sided dice are rolled.

Give any introductory information the student needs.

			Name	Type	Generated Value

number

integer

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Name

Data type

Value

xxxxxxxxxx
 
random(1..6)

JME function reference

Description

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

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Generated value: `integer`

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"Unnamed part" - prompt

Parts

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1. Gap Mathematical expression
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Gap-fill

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

What is the probability of at least one die showing a $\var{number}$ ?

Probability = Unnamed gap

Enter your answer as a fraction and not a decimal.

Advice

Let $A$ be the event that first dice shows a $\var{number}$ $\Rightarrow P(A)=\frac{1}{6}$.

Let $B$ be the event that second dice shows a $\var{number}$ $\Rightarrow P(B)=\frac{1}{6}$.

$A$ and $B$ are independent events so $P(A\cap B) = P(A)\times P(B)$.

We want the probability $P(A \cup B)$ of either $A$ or $B$ showing $\var{number}$ and

\[\begin{eqnarray*} P(A \cup B) &=& P(A)+P(B)-P(A \cap B)\\ &=& P(A)+P(B)-P(A)P(B)\\ &=&\frac{1}{6}+ \frac{1}{6}-\frac{1}{36}\\ &=& \frac{11}{36} \end{eqnarray*} \]

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This question is used in the following exams:

Introduction to Probability by Katie Bullen in Katie's workspace.
LS4003 Maths Test 2B (2018-19) by Nigel Atkins in Nigel's workspace.
Maths Test 2B (2019-20) by Nigel Atkins in Nigel's workspace.

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Roll a pair of dice - find probability at least one die shows a given number, , ,

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Nigel Atkins 8 years ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Error

Roll a pair of dice - find probability at least one die shows a given number, , ,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Nigel Atkins 8 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`