Aine 's copy of Select a card and roll a dice

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Aine Ni She

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Aine Ni She 7 years, 9 months ago

Created this as a copy of Select a card and roll a dice.

Name	Status	Author	Last Modified
Select a card and roll a dice	Ready to use	Julie Crowley	14/03/2023 08:23
Julie's copy of Select a card and roll a dice	draft	Julie Crowley	13/02/2017 15:43
Catherine's copy of Julie's copy of Select a card and roll a dice	draft	Catherine Palmer	06/04/2017 11:11
Aine 's copy of Select a card and roll a dice	draft	Aine Ni She	11/06/2017 19:14
Julie's copy of Select a card and roll a dice	draft	Julie Crowley	06/02/2018 14:09
Simon's copy of Select a card and roll a dice	draft	Simon Thomas	13/05/2019 09:23
Maria's copy of Select a card and roll a dice	draft	Maria Aneiros	27/05/2019 02:43

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Question statement

Please give your answers to 3 decimal places.

A student selects one card at random from a pack of 52 playing cards and then rolls a dice once.

Let event $A$ be that the card she picks is a $\var{suit}$ .

Let event $B$ be that the number she rolls is greater than $\var{n}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

			n	integer	2
			suit	string	club

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..4)

JME function reference

Description

number on dice is greater than n.

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

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Advice

The outcome of selecting the card is independent of (not effected by) the outcome of rolling the dice.

If two events, $A$ and $B$ , are independent then $P(A\cap B)=P(A)\times P(B)$ .

Part a)

Let $A$ represent the event that a $\var{suit}$ is selected and let $B$ represent the event that a number greater than $\var{n}$ is rolled.

$P(A)$ is $\frac{13}{52}=\frac{1}{4}$ and $P(B)$ is $\frac{\var{6-n}}{6}$ .

Therefore the probability of drawing a $\var{suit}$ and rolling a number greater than $\var{n}$ is $P(A) \times P(B)=\frac{1}{4} \times \frac{\var{6-n}}{6}$ .

Part b)

The probability that neither of these events occur is the probability of not drawing a $\var{suit}$ which is $P(A^c)=\frac{3}{4}$ mulitiplied by the probability of not rolling a number greater than $\var{n}$ which is $P(B^c)=\frac{\var{n}}{6}$ .

Part c)

The probability that only one of these events occur is $P(A ^c\cap B)+P(A \cap B^c)=(\frac{3}{4} \times \frac{\var{6-n}}{6})+(\frac{1}{4} \times \frac{\var{n}}{6})$ .

Part d)

The probability that at least one of these two events will occur is $1- P$ (neither of the events occur) $=1-(P(A^c)\times P(B^c))= 1-(\frac{3}{4}\times \frac{\var{n}}{6})$

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Aine 's copy of Select a card and roll a dice

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Aine Ni She 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Number entry

Advanced settings

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Error

Aine 's copy of Select a card and roll a dice

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Aine Ni She 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`