An eight-sided dice numbered from 1 to 8 is rolled 80 times to determine whether it is fair. The results obtained were: Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 Relative frequency Copy and complete the table with the relative frequency of each of the possible outcomes. Give your answers to 3 significant figures.

Given that, Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 Relative frequency of event = frequency of an event total frequency Total frequency = 80 Therefore, relative frequency table is as given below Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 Relative frequency 0 . 1 0 . 1 0 . 15 0 . 137 0 . 1375 0 . 15 0 . 1375 0 . 0875

An eight-sided dice numbered from 1 to 8 is rolled 80 times to determine whether it is fair. The results obtained were: Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 The dice is rolled 320 times more. Number on dice 1 2 3 4 5 6 7 8 Frequency 29 41 43 39 45 46 32 45 Using the combined data from the two tables, determine the relative frequency for each possible outcome.

When dice is thrown 80 times, we get Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 When dice is thrown 320 times Number on dice 1 2 3 4 5 6 7 8 Frequency 29 41 43 39 45 46 32 45 To get combined frequencies, we need to add frequencies. Number on dice 1 2 3 4 5 6 7 8 Frequency 37 49 55 50 56 58 43 52 Relative frequency of event = frequency of an event total frequency Total frequency = 320 + 80 = 400 Number on dice 1 2 3 4 5 6 7 8 Frequency 37 49 55 50 56 58 43 52 Relative frequency 0 . 0925 0 . 1225 0 . 1375 0 . 125 0 . 14 0 . 145 0 . 1075 0 . 13

An eight-sided dice numbered from 1 to 8 is rolled 80 times to determine whether it is fair. The results obtained were: Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 The dice is rolled 320 times more. Number on dice 1 2 3 4 5 6 7 8 Frequency 29 41 43 39 45 46 32 45 Using the combined data from the two tables, determine the relative frequency for each possible outcome. Conclude from the data whether the dice is fair.

When dice is thrown 80 times, we get Number on dice 1 2 3 4 5 6 7 8 Frequency 8 8 12 11 11 12 11 7 When dice is thrown 320 times Number on dice 1 2 3 4 5 6 7 8 Frequency 29 41 43 39 45 46 32 45 To get combined frequencies, we need to add frequencies. Number on dice 1 2 3 4 5 6 7 8 Frequency 37 49 55 50 56 58 43 52 Relative frequency of event = frequency of an event total frequency Total frequency = 320 + 80 = 400 Number on dice 1 2 3 4 5 6 7 8 Frequency 37 49 55 50 56 58 43 52 Relative frequency 0 . 0925 0 . 1225 0 . 1375 0 . 125 0 . 14 0 . 145 0 . 1075 0 . 13 A fair experiment results in equal relative frequency for all possible outcomes. Therefore, the dice is not fair.

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An eight-sided dice numbered from $1$ to $8$ is rolled $80$ times to determine whether it is fair.

If the dice is fair, how many of each number would you expect to get?

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Important Questions on Quantifying Randomness: Probability

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8B>Q 3

An eight-sided dice numbered from $1$ to $8$ is rolled $80$ times to determine whether it is fair.

The results obtained were:

Number on dice	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency	$8$	$8$	$12$	$11$	$11$	$12$	$11$	$7$
Relative frequency

Copy and complete the table with the relative frequency of each of the possible outcomes. Give your answers to $3$ significant figures.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8B>Q 3

An eight-sided dice numbered from $1$ to $8$ is rolled $80$ times to determine whether it is fair.

The results obtained were:

Number on dice	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency	$8$	$8$	$12$	$11$	$11$	$12$	$11$	$7$

The dice is rolled $320$ times more.

Number on dice	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency	$29$	$41$	$43$	$39$	$45$	$46$	$32$	$45$

Using the combined data from the two tables, determine the relative frequency for each possible outcome.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8B>Q 3

An eight-sided dice numbered from $1$ to $8$ is rolled $80$ times to determine whether it is fair.

The results obtained were:

Number on dice	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency	$8$	$8$	$12$	$11$	$11$	$12$	$11$	$7$

The dice is rolled $320$ times more.

Number on dice	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency	$29$	$41$	$43$	$39$	$45$	$46$	$32$	$45$

Using the combined data from the two tables, determine the relative frequency for each possible outcome.

Conclude from the data whether the dice is fair.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8C>Q 1

In a group of $38$ students, $29$ play computer games, $10$ play board games and $9$ play both.

Draw a Venn diagram to represent this situation.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8C>Q 1

In a group of $38$ students, $29$ play computer games, $10$ play board games and $9$ play both.

A student is selected at random. Find the probability that the student plays neither computer games nor board games.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8C>Q 2

In a sports club, $40$ members play badminton, $37$ members play squash, $21$ play both and $7$ play neither.

Represent this information in a Venn diagram.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8C>Q 2

In a sports club, $40$ members play badminton, $37$ members play squash, $21$ play both and $7$ play neither.

Represent this information in a Venn diagram. Determine how many people are members of the club.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 8 - Quantifying Randomness: Probability>Exercise 8C>Q 2

In a sports club, $40$ members play badminton, $37$ members play squash, $21$ play both and $7$ play neither.

Represent this information in a Venn diagram. Determine the probability that a member plays badminton.

An eight-sided dice numbered from 1 to 8 is rolled 80 times to determine whether it is fair. If the dice is fair, how many of each number would you expect to get?

Important Questions on Quantifying Randomness: Probability

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An eight-sided dice numbered from $1$ to $8$ is rolled $80$ times to determine whether it is fair.

If the dice is fair, how many of each number would you expect to get?