Probability, NAPX9-TLD-CA20 SA v3

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

633

Question

Michael rolled a standard dice 76 times.

He wrote down if he rolled an odd or even number each time, and recorded the results in the table below.


Result Number of times
Odd 32
Even 44


What is the difference between the expected number of odd numbers and the actual number recorded?

Worked Solution

Probability of odd = 36\dfrac{3}{6} = 12\dfrac{1}{2}

Expected number of odd numbers
= 12×76\dfrac{1}{2} \times 76
= 38

∴\therefore Difference = 38 −- 32
= 6

Question Type

Answer Box

Variables

Variable nameVariable value
question
Michael rolled a standard dice 76 times. He wrote down if he rolled an odd or even number each time, and recorded the results in the table below.
>>| Result| Number of times | |:-:|:-:| | Odd | 32| | Even| 44|

What is the difference between the expected number of odd numbers and the actual number recorded?
workedSolution
Probability of odd = $\dfrac{3}{6}$ = $\dfrac{1}{2}$ sm_nogap Expected number of odd numbers
>| | | | ------------- | ---------- | | | \= $\dfrac{1}{2} \times 76$ | | | \= 38 |

| | | | ------------: | ---------- | | $\therefore$ Difference | \= 38 $-$ 32 | | | \= {{{correctAnswer0}}} |
correctAnswer0
6
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
correctAnswer06

Variant 1

DifficultyLevel

631

Question

Penelope flipped a fair coin 128 times.

She wrote whether the toss was a head or tail each time, and recorded the results in the table below.


Result Number of times
Head 53
Tail 75


What is the difference between the expected number of tails and the actual number recorded?

Worked Solution

Probability of tail = 12\dfrac{1}{2}

Expected number of tails
= 12×128\dfrac{1}{2} \times 128
= 64

∴\therefore Difference = 75 −- 64
= 11

Question Type

Answer Box

Variables

Variable nameVariable value
question
Penelope flipped a fair coin 128 times. She wrote whether the toss was a head or tail each time, and recorded the results in the table below.
>>| Result| Number of times | |:-:|:-:| | Head | 53| | Tail| 75|

What is the difference between the expected number of tails and the actual number recorded?
workedSolution
Probability of tail = $\dfrac{1}{2}$ sm_nogap Expected number of tails
>| | | | ------------- | ---------- | | | \= $\dfrac{1}{2} \times 128$ | | | \= 64 |

| | | | ------------: | ---------- | | $\therefore$ Difference | \= 75 $-$ 64 | | | \= {{{correctAnswer0}}} |
correctAnswer0
11
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
correctAnswer011

Variant 2

DifficultyLevel

641

Question

Jevin rolled a standard dice 93 times.

He wrote down if he rolled a number above two each time, and recorded the results in the table below.


Result Number of times
Above 2 56
Not above 2 37


What is the difference between the expected number of rolls that produced a number above two and the actual number recorded?

Worked Solution

Possible results = 1, 2, 3, 4, 5 or 6

Number of results above 2 = 4

Probability of above 2 = 46\dfrac{4}{6} = 23\dfrac{2}{3}

Expected number rolls above 2
= 23×93\dfrac{2}{3} \times 93
= 6

∴\therefore Difference = 62 −- 56
= 6

Question Type

Answer Box

Variables

Variable nameVariable value
question
Jevin rolled a standard dice 93 times. He wrote down if he rolled a number above two each time, and recorded the results in the table below.
>>| Result| Number of times | |:-:|:-:| | Above 2 | 56| | Not above 2| 37|

What is the difference between the expected number of rolls that produced a number above two and the actual number recorded?
workedSolution
Possible results = 1, 2, 3, 4, 5 or 6 Number of results above 2 = 4 Probability of above 2 = $\dfrac{4}{6}$ = $\dfrac{2}{3}$ sm_nogap Expected number rolls above 2
>| | | | ------------- | ---------- | | | \= $\dfrac{2}{3} \times 93$ | | | \= {{{correctAnswer0}}} |

| | | | ------------: | ---------- | | $\therefore$ Difference | \= 62 $-$ 56 | | | \= {{{correctAnswer0}}} |
correctAnswer0
6
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
correctAnswer06

Variant 3

DifficultyLevel

652

Question

Campbell rolled a standard dice 15 times.

He wrote down what number he rolled each time, and recorded the results in the table below.


Result Number of times
1 or 2 3
3 or 4 5
5 or 6 7


What is the difference between the expected number of times he rolled a 5 or 6, and the actual number of times recorded?

Worked Solution

Probability of 5 or 6 = 26\dfrac{2}{6} = 13\dfrac{1}{3}

Expected number of rolls
= 13×15\dfrac{1}{3} \times 15
= 5

∴\therefore Difference = 7 −- 5
= 2

Question Type

Answer Box

Variables

Variable nameVariable value
question
Campbell rolled a standard dice 15 times. He wrote down what number he rolled each time, and recorded the results in the table below.
>>| Result| Number of times | |:-:|:-:| | 1 or 2| 3| | 3 or 4| 5| | 5 or 6| 7|

What is the difference between the expected number of times he rolled a 5 or 6, and the actual number of times recorded?
workedSolution
Probability of 5 or 6 = $\dfrac{2}{6}$ = $\dfrac{1}{3}$ sm_nogap Expected number of rolls
>| | | | ------------- | ---------- | | | \= $\dfrac{1}{3} \times 15$ | | | \= 5 |

| | | | ------------: | ---------- | | $\therefore$ Difference | \= 7 $-$ 5 | | | \= {{{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

Variant 4

DifficultyLevel

634

Question

James flipped a fair coin 42 times.

He wrote down if it was a head or tail each time, and recorded the results in the table below.


Result Number of times
Head 17
Tail 25


What is the difference between the expected number of tails and the actual number recorded?

Worked Solution

Probability of tail = 12\dfrac{1}{2}

Expected number of tails
= 12×42\dfrac{1}{2} \times 42
= 21

∴\therefore Difference = 25 −- 21
= 4

Question Type

Answer Box

Variables

Variable nameVariable value
question
James flipped a fair coin 42 times. He wrote down if it was a head or tail each time, and recorded the results in the table below.
>>| Result| Number of times | |:-:|:-:| | Head| 17| | Tail| 25|

What is the difference between the expected number of tails and the actual number recorded?
workedSolution
Probability of tail = $\dfrac{1}{2}$ sm_nogap Expected number of tails
>| | | | ------------- | ---------- | | | \= $\dfrac{1}{2} \times 42$ | | | \= 21 |

| | | | ------------: | ---------- | | $\therefore$ Difference | \= 25 $-$ 21 | | | \= {{{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

628

Question

Yoshi rolled a standard dice 26 times.

He wrote down if he rolled an odd or an even number each time, and recorded the results in the table below.


Result Number of times
Odd 16
Even 10


What is the difference between the expected number of rolls that produced an even number and the actual number recorded?

Worked Solution

Probability of even = 36\dfrac{3}{6} = 12\dfrac{1}{2}

Expected number of even rolls
= 12×26\dfrac{1}{2} \times 26
= 13

∴\therefore Difference = 13 −- 10
= 3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Yoshi rolled a standard dice 26 times. He wrote down if he rolled an odd or an even number each time, and recorded the results in the table below.
>>| Result| Number of times | |:-:|:-:| | Odd | 16| | Even| 10|

What is the difference between the expected number of rolls that produced an even number and the actual number recorded?
workedSolution
Probability of even = $\dfrac{3}{6}$ = $\dfrac{1}{2}$ sm_nogap Expected number of even rolls
>| | | | ------------- | ---------- | | | \= $\dfrac{1}{2} \times 26$ | | | \= 13 |

| | | | ------------: | ---------- | | $\therefore$ Difference | \= 13 $-$ 10 | | | \= {{{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

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