Ugur's copy of Probability of picking a particular colour ball from a bag

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Created this as a copy of Probability of picking a particular colour ball from a bag.

Name	Status	Author	Last Modified
Basic Probability Questions	Should not be used	Elliott Fletcher	20/11/2019 14:33
Choose the probability of getting certain scores on a die	Ready to use	Christian Lawson-Perfect	20/11/2019 14:34
Probability of flipping a coin and getting a tails	Ready to use	Christian Lawson-Perfect	20/11/2019 14:41
Probability of picking a particular colour ball from a bag	Ready to use	Christian Lawson-Perfect	20/11/2019 14:41
Maria's copy of Choose the probability of getting certain scores on a die	draft	Maria Aneiros	27/05/2019 02:29
Maria's copy of Probability of picking a particular colour ball from a bag	draft	Maria Aneiros	27/05/2019 02:32
Choose the probability of getting certain scores on a die	draft	Xiaodan Leng	11/07/2019 01:57
Probability of flipping a coin and getting a tails	draft	Xiaodan Leng	11/07/2019 01:58
Probability of picking a particular colour ball from a bag	draft	Xiaodan Leng	11/07/2019 01:58
Ugur's copy of Probability of picking a particular colour ball from a bag	Ready to use	Ugur Efem	28/04/2022 11:04

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

red	integer	18
blue	integer	7
green	integer	5
total	integer	30
a	integer	1
red1	integer	5
b	integer	6
ansb	rational	1
red2	integer	19
blue2	integer	8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(15,16,17,18,19)

JME function reference

Description

number of red balls in part c

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`

→ Used by:

red2
total

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Choose one from a list
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Part b) Gap-fill
1. Gap Gap 0 Mathematical expression
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Part c) Gap-fill
1. Gap Number entry
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Ask the student a question, and give any hints about how they should answer this part.

A bag contains $\var{red}$ red balls, $\var{blue}$ blue balls and $\var{green}$ green balls. One ball is chosen from the bag at random. What is the probability that the chosen ball will be blue?

Unnamed gap

Advice

a)For equally likely outcomes, you can calculate the probability of a particular event occurring by using the formula

$\text{Probability of an event} = \displaystyle\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ .

We are told that the bag contains $\var{red}$ red balls, $\var{blue}$ blue balls and $\var{green}$ green balls and that one ball is removed from the bag at random.

The total number of balls in the bag before the chosen ball is removed is

$\var{red}+\var{blue}+\var{green} = \var{total}.$

As the ball is being removed randomly from the bag, there is an equal probability of selecting any one of the $\var{total}$ balls.

Therefore, the probability of the chosen ball being blue is

$P(\text{blue}) = \displaystyle\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}} = \displaystyle\frac{\var{blue}}{\var{total}}$

b) In total there are $\var{red1} + n$ balls. Probability choosing one green ball is therefore $\frac{n}{\var{red1} + n}$ .

We are given that $\frac{n}{\var{red1} + n} = \frac{\var{a}}{\var{b}}$ . Cross multiplication gives $\var{b}n = \var{a}\times\var{red1} + \var{a}n$ .

Simplfying yields $n = \var{ansb}$

c) In total there are $\var{red2}+\var{blue2} +\var{green}$ balls. Probability of picking a red ball is $\frac{\var{red2}}{\var{red2}+\var{blue2} +\var{green}}$ . Probability of picking a blue ball is $\frac{\var{blue2}}{\var{red2}+\var{blue2} +\var{green}}$ . Total probability is tehir sum:

$\frac{\var{red2}+\var{blue2}}{\var{red2}+\var{blue2} +\var{green}}.$

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Ugur's copy of Probability of picking a particular colour ball from a bag

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Taxonomy: mathcentre

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Taxonomy: Context

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Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Ugur's copy of Probability of picking a particular colour ball from a bag

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`