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PROBLEMS VIEWING PRESENTATION PowerPoint XP  PowerPoint 2007 PowerPoint 2010 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 2007. 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. http://www.microsoft.com/downloads/en/details.aspx?FamilyID=cb9bf144-1076-4615-9951-294eeb832823 If you require further information on the problem, you can visit Microsoft Support at http://support.microsoft.com/kb/941878 where they supply a “HOT FIX” for this problem, should you wish to use it.

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 = 0.06 250 trials 350 trials

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 350 trials

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. 250 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

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 2000 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 = 0.06 350 trials

? 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 0.016 or 1.6% (c) Yellow = 115/500 = 0.23. So 0.23 x 1800 = 414

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

Theoretical Probability 4 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

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

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

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

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

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

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