1. Whiteboardmaths.com
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2. PROBLEMS VIEWING PRESENTATION
PowerPoint XP 
PowerPoint 2007
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PowerPoint Viewer
Slides 8. 9 and 10 show the three spinners (with animations) as shown below. For some unknown reason, only the pink spinner is visible with PowerPoint It is hoped that service pack 3 may fix the problem when it becomes available. In the meantime it is suggested that you do one of the following:
Use the three “screen shots” of these slides (no animation) together with the questions and answers that have been added as slides 11, 12 and 13.
Download the free PowerPoint Viewer using the first link below.
If you require further information on the problem, you can visit Microsoft Support at where they supply a “HOT FIX” for this problem, should you wish to use it.

3. Probability: Relative Frequency
An estimate of the probability of an event happening can be obtained by looking back at experimental or statistical data to obtain relative frequency.
Experiment
Data(Survey)
Throws of a biased die.
Colour of cars passing traffic lights. 95 6 34 5 30 4 32 3 2 25 1
Relative freq
freq No
Colour
freq
Relative freq
Red 50
Blue 80
Green 30
White 40
Silver
130
Black 20
25/250 = 0.1
50/350 = 0.14
34/250 = 0.136
80/350 = 0.23
32/250 = 0.128
30/350 = 0.09
30/250 = 0.12
40/350 = 0.11
34/250 = 0.136
130/350 = 0.37
95/250 = 0.38
20/350 = 0.06
trials
350 trials

4. Probability: Relative Frequency
Experiment
Data(Survey)
Throws of a biased die.
Colour of cars passing traffic lights. 95 6 34 5 30 4 32 3 2 25 1
Relative freq
freq No
Colour
freq
Relative freq
Red 50
Blue 80
Green 30
White 40
Silver
130
Black 20
The probability of the next throw being a 1 is approximately 0.1 or 10%
25/250 = 0.1
50/350 = 0.14
The probability of the next car being blue is approximately 0.23 or 23%
34/250 = 0.136
80/350 = 0.23
32/250 = 0.128
30/350 = 0.09
30/250 = 0.12
40/350 = 0.11
The probability of the next car being silver is approximately 0.37 or 37%
34/250 = 0.136
130/350 = 0.37
The probability of the next throw being a 6 is approximately 0.38 or 38%
95/250 = 0.38
20/350 = 0.06
250 trials
trials

5. Probability: Relative Frequency
Relative frequency can be used to estimate the number of times that an event is likely to occur within a given number of trials.
Experiment
Throws of a biased die.
trials 95 6 34 5 30 4 32 3 2 25 1
Relative freq
freq No
25/250 = 0.1
34/250 = 0.136
32/250 = 0.128
30/250 = 0.12
95/250 = 0.38
Use the information in the table to estimate the frequency of each number on the die for 1800 throws.
0.1 x 1800 = 180
0.136 x 1800 = 245
0.128 x 1800 = 230
0.12 x 1800 = 216
0.38 x 1800 = 684

6. Probability: Relative Frequency
Relative frequency can be used to estimate the number of times that an event is likely to occur within a given number of trials.
Use the information in the table to estimate the frequency of each car colour if cars passed through the traffic lights.
Data(Survey)
Colour of cars passing traffic lights.
Colour
freq
Relative freq
Red 50
Blue 80
Green 30
White 40
Silver
130
Black 20
Red = 0.14 x 2000 = 280
Blue = 0.23 x 2000 = 460
Green = 0.09 x 2000 = 180
White = 0.11 x 2000 = 220
Silver = 0.37 x 2000 = 740
Black = 0.06 x 2000 = 120
50/350 = 0.14
80/350 = 0.23
30/350 = 0.09
40/350 = 0.11
130/350 = 0.37
20/350 = 0.06
trials

7. ? Probability: Relative Frequency
Worked Example Question: A bag contains an unknown number of coloured discs. Rebecca selects a disc at random from the bag, notes its colour, then replaces it. She does this 500 times and her results are recorded in the table below. Rebecca hands the bag to Peter who is going to select one disc from the bag. Use the information from the table to find estimates for:
The probability that Peter selects a red disc.
The probability that he selects a blue disc.
The number of yellow discs that Rebecca could expect for 1800 trials. ?
Blue
Green
Red
Yellow
White 8 85
200
115 92
(a) P(Red) = 200/500 = 2/5 or 0.4 or 40%
(b) P(Blue) = 8/500 = 2/125 or or 1.6%
(c) Yellow = 115/500 = So 0.23 x 1800 = 414

8. Theoretical Probability
Probability: Relative Frequency
Theoretical Probability
Relative frequency can also be determined for situations involving theoretical probability. 4 1 2 3 7 6 5 8 9
Pentagonal Spinner: Relative frequency = 2/5
The sections on each spinner are of equal area. State the relative frequency for the number indicated on each pointer.
Hexagonal Spinner: Relative frequency = ½
Octagonal Spinner: Relative frequency = 5/8

9. Theoretical Probability4 1 2 3 7 6 5 8 9
Probability: Relative Frequency
Theoretical Probability
Relative frequency can also be determined for situations involving theoretical probability.
280 Spins
500 Spins
720 Spins
Pentagonal Spinner: Number of 4’s expected = 2/5 x 280 = 112
Each of the pointers is spun a different number of times as shown. Calculate an estimate for the number of times that you would expect the pointer to land on the indicated number.
Hexagonal Spinner: Number of 5’s expected = ½ x 500 = 250
Octagonal Spinner: Number of 9’s expected = 5/8 x 720 = 450

10. Theoretical Probability
Probability: Relative Frequency
Theoretical Probability
Relative frequency can also be determined for situations involving theoretical probability. 6 2 3 8 5 7 4
400 Spins
270 Spins
560 Spins
Pentagonal Spinner: Number of 6’s expected = 3/5 x 400 = 240
Each of the pointers is spun a different number of times as shown. Calculate an estimate for the number of times that you would expect the pointer to land on the indicated number.
Hexagonal Spinner: Number of 2’s expected = 2/3 x 270 = 180
Octagonal Spinner: Number of 7’s expected = 3/8 x 560 = 210

11. Pentagonal Spinner: Relative frequency = 2/5
Hexagonal Spinner: Relative frequency = ½
Octagonal Spinner: Relative frequency = 5/8

12. Pentagonal Spinner: Number of 4’s expected = 2/5 x 280 = 112
Hexagonal Spinner: Number of 5’s expected = ½ x 500 = 250
Octagonal Spinner: Number of 9’s expected = 5/8 x 720 = 450

13. Pentagonal Spinner: Number of 6’s expected = 3/5 x 400 = 240
Hexagonal Spinner: Number of 2’s expected = 2/3 x 270 = 180
Octagonal Spinner: Number of 7’s expected = 3/8 x 560 = 210

14. Worksheet 1 Probability: Relative Frequency Experiment Data(Survey)
Throws of a biased die.
Colour of cars passing traffic lights. 95 6 34 5 30 4 32 3 2 25 1
Relative freq
freq No
Colour
freq
Relative freq
Red 50
Blue 80
Green 30
White 40
Silver
130
Black 20
Worksheet 1

15. Worksheet 2 95 6 34 5 30 4 32 3 2 25 1 Relative freq freq No
25/250 = 0.1
34/250 = 0.136
32/250 = 0.128
30/250 = 0.12
34/250 = 0.136
95/250 = 0.38
Colour
freq
Relative freq
Red 50
Blue 80
Green 30
White 40
Silver
130
Black 20
50/350 = 0.14
80/350 = 0.23
30/350 = 0.09
Worksheet 2
40/350 = 0.11
130/350 = 0.37
20/350 = 0.06