Probability, NAPX-p110739v02 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

627

Question

Shawn has a bag that holds one blue ball, one red ball and one green ball.

Shawn picks one ball without looking, records its colour and puts it back in the bag.

He repeated this process 60 times and summarises the results in the table below.


Colour Number of Times
Red 23
Blue 19
Green 18

What is the difference between the expected and actual number of red balls picked?

Worked Solution

Probability of grabbing a red ball = 13\dfrac{1}{3}
Expected number of red balls = 13 ×60\dfrac{1}{3} \ \times 60
= 20

∴\therefore Difference = 23 − 2023 \ − \ 20
= 3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Shawn has a bag that holds one blue ball, one red ball and one green ball. Shawn picks one ball without looking, records its colour and puts it back in the bag. He repeated this process 60 times and summarises the results in the table below.
>>> |Colour |Number of Times| |:-:|:-:| |Red|23| |Blue|19| |Green|18|

What is the difference between the expected and actual number of red balls picked?
workedSolution
Probability of grabbing a red ball = $\dfrac{1}{3}$
| | | | ------------- | ---------- | | Expected number of red balls | \= $\dfrac{1}{3} \ \times 60$ | | | \= 20 |

| | | | ------------- | ---------- | | $\therefore$ Difference | \= $23 \ − \ 20$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
3
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer03

Variant 1

DifficultyLevel

625

Question

Elaine rolled a regular die 100 times.

She recorded if an even or odd number appeared each time.

The table below represents the recorded data.


Result Number of Times
Even 58
Odd 42

What is the difference between the expected number of odd rolls to the actual odd rolls recorded?

Worked Solution

Probability of odd number = 36\dfrac{3}{6} = 50%
Expected number of odd rolls = 50% ×\times 100
= 50

∴\therefore Difference = 50 − 4250 \ − \ 42
= 8

Question Type

Answer Box

Variables

Variable nameVariable value
question
Elaine rolled a regular die 100 times. She recorded if an even or odd number appeared each time. The table below represents the recorded data.
>>> |Result |Number of Times| |:-:|:-:| |Even|58| |Odd|42|

What is the difference between the expected number of odd rolls to the actual odd rolls recorded?
workedSolution
Probability of odd number = $\dfrac{3}{6}$ = 50%
| | | | ------------- | ---------- | | Expected number of odd rolls | \= 50% $\times$ 100 | | | \= 50 |

| | | | ------------- | ---------- | | $\therefore$ Difference | \= $50 \ − \ 42$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
8
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer08

Variant 2

DifficultyLevel

629

Question

Geoff has a bag that holds one orange ball, one red ball, one white ball and one green ball.

Geoff picks one ball without looking, records its colour and puts it back in the bag.

He repeated this process 60 times and summarises the results in the table below.


Colour Number of Times
Orange 19
Red 12
White 15
Green 14

What is the difference between the expected and actual number of orange balls picked?

Worked Solution

Probability of grabbing an orange ball = 14\dfrac{1}{4}
Expected number of orange balls = 14 ×60\dfrac{1}{4} \ \times 60
= 15

∴\therefore Difference = 19 − 1519 \ − \ 15
= 4

Question Type

Answer Box

Variables

Variable nameVariable value
question
Geoff has a bag that holds one orange ball, one red ball, one white ball and one green ball. Geoff picks one ball without looking, records its colour and puts it back in the bag. He repeated this process 60 times and summarises the results in the table below.
>>> |Colour |Number of Times| |:-:|:-:| |Orange|19| |Red|12| |White|15| |Green|14|

What is the difference between the expected and actual number of orange balls picked?
workedSolution
Probability of grabbing an orange ball = $\dfrac{1}{4}$
| | | | ------------- | ---------- | | Expected number of orange balls | \= $\dfrac{1}{4} \ \times 60$ | | | \= 15 |

| | | | ------------- | ---------- | | $\therefore$ Difference | \= $19 \ − \ 15$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
4
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer04

Variant 3

DifficultyLevel

631

Question

Tammy rolls a fair dice with six faces numbered 1 to 6.

She repeated this process 30 times and the results are summarised in the table below.


Number Number of Times
1 5
2 3
3 8
4 6
5 3
6 5

What is the difference between the expected and actual number of times that number 3 was rolled?

Worked Solution

Probability of rolling a 3 = 16\dfrac{1}{6}
Expected number of 3's = 16 ×30\dfrac{1}{6} \ \times 30
= 5

∴\therefore Difference = 8 − 58 \ − \ 5
= 3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Tammy rolls a fair dice with six faces numbered 1 to 6. She repeated this process 30 times and the results are summarised in the table below.
>>> |Number|Number of Times| |:-:|:-:| |1|5| |2|3| |3|8| |4|6| |5|3| |6|5|

What is the difference between the expected and actual number of times that number 3 was rolled?
workedSolution
Probability of rolling a 3 = $\dfrac{1}{6}$
| | | | ------------- | ---------- | | Expected number of 3's | \= $\dfrac{1}{6} \ \times 30$ | | | \= 5 |

| | | | ------------- | ---------- | | $\therefore$ Difference | \= $8 \ − \ 5$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
3
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer03

Variant 4

DifficultyLevel

634

Question

Keiron rolls a fair dice with six faces numbered 1 to 6.

He repeated this process 42 times and the results are summarised in the table below.


Number Number of Times
1 7
2 5
3 11
4 7
5 6
6 6

What is the difference between the expected and actual number of times that number 3 was rolled?

Worked Solution

Probability of rolling a 3 = 16\dfrac{1}{6}
Expected number of 3's = 16 ×42\dfrac{1}{6} \ \times 42
= 7

∴\therefore Difference = 11 − 711 \ − \ 7
= 4

Question Type

Answer Box

Variables

Variable nameVariable value
question
Keiron rolls a fair dice with six faces numbered 1 to 6. He repeated this process 42 times and the results are summarised in the table below.
>>> |Number|Number of Times| |:-:|:-:| |1|7| |2|5| |3|11| |4|7| |5|6| |6|6|

What is the difference between the expected and actual number of times that number 3 was rolled?
workedSolution
Probability of rolling a 3 = $\dfrac{1}{6}$
| | | | ------------- | ---------- | | Expected number of 3's | \= $\dfrac{1}{6} \ \times 42$ | | | \= 7 |

| | | | ------------- | ---------- | | $\therefore$ Difference | \= $11 \ − \ 7$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
4
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer04

Variant 5

DifficultyLevel

642

Question

Dolly rolls a fair dice with six faces numbered 1 to 6.

She repeated this process 48 times and the results are summarised in the table below.


Number Number of Times
1 8
2 5
3 12
4 10
5 5
6 8

What is the difference between the expected and actual number of times that number 4 was rolled?

Worked Solution

Probability of rolling a 4 = 16\dfrac{1}{6}
Expected number of 4's = 16 ×48\dfrac{1}{6} \ \times 48
= 8

∴\therefore Difference = 10 − 810 \ − \ 8
= 2

Question Type

Answer Box

Variables

Variable nameVariable value
question
Dolly rolls a fair dice with six faces numbered 1 to 6. She repeated this process 48 times and the results are summarised in the table below.
>>> |Number|Number of Times| |:-:|:-:| |1|8| |2|5| |3|12| |4|10| |5|5| |6|8|

What is the difference between the expected and actual number of times that number 4 was rolled?
workedSolution
Probability of rolling a 4 = $\dfrac{1}{6}$
| | | | ------------- | ---------- | | Expected number of 4's | \= $\dfrac{1}{6} \ \times 48$ | | | \= 8 |

| | | | ------------- | ---------- | | $\therefore$ Difference | \= $10 \ − \ 8$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
2
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer02

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