Probability, NAPX-p167310v04

Question

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Worked Solution

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Variant 0

DifficultyLevel

582

Question

A man spins a wheel with 5 different coloured sections and records which colour it lands on each time.

He repeats the process multiple times.

The table below shows the results.


WHITE YELLOW RED BLUE GREEN
42 24 38 27 37


Using the table, what is the probability that the next spin will be yellow?

Worked Solution
PP(yellow) = Number of yellowTotal number of throws\dfrac{\text{Number of yellow}}{\text{Total number of throws}}
= 2442+24+38+27+37\dfrac{24}{42+24+38+27+37}
= 24168\dfrac{24}{168}
= 17\dfrac{1}{7}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A man spins a wheel with 5 different coloured sections and records which colour it lands on each time. He repeats the process multiple times. The table below shows the results.
>> | WHITE | YELLOW | RED | BLUE | GREEN | > | :-----------: | :----------: | :------------: | :----------: | :------------: | > | 42 | 24 | 38 | 27 | 37 |


Using the table, what is the probability that the next spin will be yellow?
workedSolution
| | | | ------------: | ---------- | | $P$(yellow) | \= $\dfrac{\text{Number of yellow}}{\text{Total number of throws}}$ | | | | | | \= $\dfrac{24}{42+24+38+27+37}$ | | | | | | \= $\dfrac{24}{168}$ | | | | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{1}{7}$

Answers

Is Correct?Answer
x

631\dfrac{6}{31}

x

1684\dfrac{16}{84}

✓

17\dfrac{1}{7}

x

25\dfrac{2}{5}

Variant 1

DifficultyLevel

585

Question

Marie grabs a coloured ball from a bag and records the colour. She then puts the ball back into the bag and repeats this process 96 times.

The results are shown in the table below.

Orange Blue Red Green White Black Yellow
13 20 18 9 12 14 10

Using the table, what is the probability that the next ball picked out by Marie will be yellow?

Worked Solution
PP(yellow) = Number of yellowTotal number\dfrac{\text{Number of yellow}}{\text{Total number}}
= 1096\dfrac{10}{96}
= 548\dfrac{5}{48}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Marie grabs a coloured ball from a bag and records the colour. She then puts the ball back into the bag and repeats this process 96 times. The results are shown in the table below.
>> | Orange | Blue | Red | Green| White | Black | Yellow | > | :-----------: | :----------: | :------------: | :----------: | :------------: | :----------: | :------------: | > | 13 | 20 | 18 | 9 | 12 | 14 | 10 |

Using the table, what is the probability that the next ball picked out by Marie will be yellow?
workedSolution
| | | | ------------: | ---------- | | $P$(yellow) | \= $\dfrac{\text{Number of yellow}}{\text{Total number}}$ | | | \= $\dfrac{10}{96}$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{5}{48}$

Answers

Is Correct?Answer
✓

548\dfrac{5}{48}

x

625\dfrac{6}{25}

x

543\dfrac{5}{43}

x

736\dfrac{7}{36}

Variant 2

DifficultyLevel

580

Question

A biased die has 6 faces numbered from 1 to 6.

Raven throws the die 50 times and recorded the results in the table below.


Number 1 2 3 4 5 6
Times 11 8 9 10 6 6

Using the table, what is the probability that Raven will be throwing a 5 on her next throw?

Worked Solution
PP(5) = Number of 5’sTotal number of throws\dfrac{\text{Number of 5's}}{\text{Total number of throws}}
= 650\dfrac{6}{50}
= 325\dfrac{3}{25}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A biased die has 6 faces numbered from 1 to 6. Raven throws the die 50 times and recorded the results in the table below.
>> | Number | 1 | 2 | 3| 4 | 5 | 6 | > | :-----------: | :----------: | :------------: | :----------: | :------------: | :----------: | :------------: | > | **Times**| 11 | 8 | 9 | 10 | 6 | 6 |

Using the table, what is the probability that Raven will be throwing a 5 on her next throw?
workedSolution
| | | | ------------: | ---------- | | $P$(5) | \= $\dfrac{\text{Number of 5's}}{\text{Total number of throws}}$ | | | | | | \= $\dfrac{6}{50}$ | | | | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{3}{25}$

Answers

Is Correct?Answer
x

644\dfrac{6}{44}

x

217\dfrac{2}{17}

x

1125\dfrac{11}{25}

✓

325\dfrac{3}{25}

Variant 3

DifficultyLevel

579

Question

Peggy picks a marble from a bag and records its colour before placing it back in the bag.

She repeats this 20 times.

Her results are in the table below.


Black Green Yellow Blue Red
4 5 1 8 2


Using the table, what is the probability that the next marble Peggy picks will be black?

Worked Solution
PP(Black) = number of black pickedtotal picks\dfrac{\text{number of black picked}}{\text{total picks}}
= 420\dfrac{4}{20}
= 15\dfrac{1}{5}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Peggy picks a marble from a bag and records its colour before placing it back in the bag. She repeats this 20 times. Her results are in the table below.
>> | Black | Green | Yellow | Blue | Red | > | :-----------: | :----------: | :------------: | :----------: | :------------: | > | 4 | 5 | 1 | 8 | 2 |


Using the table, what is the probability that the next marble Peggy picks will be black?
workedSolution
| | | | ------------- | ---------- | | $P$(Black) | \= $\dfrac{\text{number of black picked}}{\text{total picks}}$ | | | \= $\dfrac{4}{20}$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{1}{5}$

Answers

Is Correct?Answer
x

14\dfrac{1}{4}

✓

15\dfrac{1}{5}

x

25\dfrac{2}{5}

x

110\dfrac{1}{10}

Variant 4

DifficultyLevel

589

Question

Klaus picks a ball from a bag and records the colour.

He then puts the ball back to the bag and repeats this process 70 times.

The results are shown in the table below.

Puple Blue Red Green White Pink
9 12 21 15 5 8

Using the table, what is the probability that the next ball picked up by Klaus will be white?

Worked Solution
PP(white) = Number of whiteTotal number\dfrac{\text{Number of white}}{\text{Total number}}
= 570\dfrac{5}{70}
= 114\dfrac{1}{14}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Klaus picks a ball from a bag and records the colour. He then puts the ball back to the bag and repeats this process 70 times. The results are shown in the table below.
>> | Puple | Blue | Red | Green| White | Pink | > | :-----------: | :----------: | :------------: | :----------: | :------------: | :----------: | > | 9 | 12 | 21 | 15 |5 | 8 |

Using the table, what is the probability that the next ball picked up by Klaus will be white?
workedSolution
| | | | ------------: | ---------- | | $P$(white) | \= $\dfrac{\text{Number of white}}{\text{Total number}}$ | | | \= $\dfrac{5}{70}$ | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{1}{14}$

Answers

Is Correct?Answer
x

565\dfrac{5}{65}

✓

114\dfrac{1}{14}

x

115\dfrac{1}{15}

x

15\dfrac{1}{5}

Variant 5

DifficultyLevel

590

Question

A biased die has 6 faces numbered from 1 to 6.

Jackson throws the die 60 times and recorded the results in the table below.


Number 1 2 3 4 5 6
Times 8 14 9 13 7 9

Using the table, what is the probability that Jackson will be throwing a 2 on his next throw?

Worked Solution
PP(2) = Number of 2’sTotal number of throws\dfrac{\text{Number of 2's}}{\text{Total number of throws}}
= 1460\dfrac{14}{60}
= 730\dfrac{7}{30}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A biased die has 6 faces numbered from 1 to 6. Jackson throws the die 60 times and recorded the results in the table below.
>> | Number | 1 | 2 | 3| 4 | 5 | 6 | > | :-----------: | :----------: | :------------: | :----------: | :------------: | :----------: | :------------: | > | **Times**| 8 | 14 | 9 | 13 | 7 | 9 |

Using the table, what is the probability that Jackson will be throwing a 2 on his next throw?
workedSolution
| | | | ------------: | ---------- | | $P$(2) | \= $\dfrac{\text{Number of 2's}}{\text{Total number of throws}}$ | | | | | | \= $\dfrac{14}{60}$ | | | | | | \= {{{correctAnswer}}} |
correctAnswer
$\dfrac{7}{30}$

Answers

Is Correct?Answer
✓

730\dfrac{7}{30}

x

1446\dfrac{14}{46}

x

15\dfrac{1}{5}

x

16\dfrac{1}{6}

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