The sides of a six-sided spinner are numbered from 1 to 6 . The table shows the results for 100 spins. Number on spinner 1 2 3 4 5 6 Frequency 27 18 17 15 16 7 Do you think the spinner is fair? Give a reason for your answer.

Given that, Number on spinner 1 2 3 4 5 6 Frequency 27 18 17 15 16 7 Relative frequency of event = frequency of an event total frequency Total frequency = 27 + 18 + 17 + 15 + 16 + 7 = 100 Number on spinner 1 2 3 4 5 6 Frequency 27 18 17 15 16 7 Relative frequency 0 . 27 0 . 18 0 . 17 0 . 15 0 . 16 0 . 07 Spinner is not fair. A fair experiment results in equal relative frequency for all possible outcomes. Therefore, spinner is not fair.

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.

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 7: Exercise 8B

Author:Natasha Awada, Paul La Rondie, Laurie Buchanan & Jill Stevens

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 7: Exercise 8B

Attempt the practice questions on Chapter 8: Quantifying Randomness: Probability, Exercise 7: Exercise 8B with hints and solutions to strengthen your understanding. Mathematics : Analysis and Approaches Standard Level Course Companion solutions are prepared by Experienced Embibe Experts.

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 7: Exercise 8B with Hints & Solutions

EASY

Diploma

IMPORTANT

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

The table shows the relative frequencies of the ages of students at a high school.

Age(years)	Relative frequency
$13$	$0.08$
$14$	$0.12$
$15$	$0.18$
$16$	$0.22$
$17$	$0.27$
$18$	$0.13$
Total	$1$

There are $1200$ students at this school. Calculate the number of $15$ -year-old students at school.

EASY

Diploma

IMPORTANT

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

The sides of a six-sided spinner are numbered from $1$ to $6$ . The table shows the results for $100$ spins.

Number on spinner	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$27$	$18$	$17$	$15$	$16$	$7$

What is the relative frequency of getting a $1$ ?

EASY

Diploma

IMPORTANT

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

The sides of a six-sided spinner are numbered from $1$ to $6$ . The table shows the results for $100$ spins.

Number on spinner	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$27$	$18$	$17$	$15$	$16$	$7$

Do you think the spinner is fair? Give a reason for your answer.

EASY

Diploma

IMPORTANT

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

The sides of a six-sided spinner are numbered from $1$ to $6$ . The table shows the results for $100$ spins.

Number on spinner	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$27$	$18$	$17$	$15$	$16$	$7$

The spinner is spun $3000$ times. Estimate the number of times the result will be a $4$ .

EASY

Diploma

IMPORTANT

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.

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

EASY

Diploma

IMPORTANT

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.

MEDIUM

Diploma

IMPORTANT

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.

MEDIUM

Diploma

IMPORTANT

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.

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 7: Exercise 8B

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 7: Exercise 8B

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Quantifying Randomness: Probability, Exercise 7: Exercise 8B with Hints & Solutions

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