2. 250 trials 350 trials 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. ColourfreqRelative freq Red50 Blue80 Green30 White40 Silver130 Black20 956 345 304 323 342 251 Relative freqfreqNoNo 25/250 = 0.1 34/250 = 0.136 32/250 = 0.128 30/250 = 0.12 34/250 = 0.136 95/250 = 0.38 50/350 = 0.14 80/350 = 0.23 30/350 = 0.09 40/350 = 0.11 130/350 = 0.37 20/350 = 0.06 Experiment Data(Survey) Throws of a biased die. Colour of cars passing traffic lights.

3. 250 trials 350 trials Probability: Relative Frequency ColourfreqRelative freq Red50 Blue80 Green30 White40 Silver130 Black20 956 345 304 323 342 251 Relative freqfreqNoNo 25/250 = 0.1 34/250 = 0.136 32/250 = 0.128 30/250 = 0.12 34/250 = 0.136 95/250 = 0.38 50/350 = 0.14 80/350 = 0.23 30/350 = 0.09 40/350 = 0.11 130/350 = 0.37 20/350 = 0.06 Experiment Data(Survey) Throws of a biased die. Colour of cars passing traffic lights. The probability of the next throw being a 6 is approximately 0.38 or 38% The probability of the next throw being a 1 is approximately 0.1 or 10% The probability of the next car being blue is approximately 0.23 or 23% The probability of the next car being silver is approximately 0.37 or 37%

4. 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 956 345 304 323 342 251 Relative freqfreqNoNo 25/250 = 0.1 34/250 = 0.136 32/250 = 0.128 30/250 = 0.12 34/250 = 0.136 95/250 = 0.38 Use the information in the table to estimate the frequency of each number on the die for 1800 throws. 1.0.1 x 1800 = 180 2.0.136 x 1800 = 245 3.0.128 x 1800 = 230 4.0.12 x 1800 = 216 5.0.136 x 1800 = 245 6.0.38 x 1800 = 684

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. Use the information in the table to estimate the frequency of each car colour if 2000 cars passed through the traffic lights. 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 Data(Survey) Colour of cars passing traffic lights. 350 trials ColourfreqRelative freq Red50 Blue80 Green30 White40 Silver130 Black20 50/350 = 0.14 80/350 = 0.23 30/350 = 0.09 40/350 = 0.11 130/350 = 0.37 20/350 = 0.06

6. Probability: Relative Frequency BlueGreenRedYellowWhite 88520011592 (a) P(Red) = 200/500 = 2/5 or 0.4 or 40% 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: (a)The probability that Peter selects a red disc. (b)The probability that he selects a blue disc. (c)The number of yellow discs that Rebecca could expect for 1800 trials. ? (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

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

8. 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. 280 Spins500 Spins720 Spins 4 1 2 3 4 7 6 5 5 8 5 3 7 9 9 9 9 9 3 Probability: Relative Frequency Theoretical Probability Relative frequency can also be determined for situations involving theoretical probability. 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

9. 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. 400 Spins270 Spins560 Spins 6 6 2 3 6 2 2 2 2 8 5 3 7 5 7 7 4 8 3 Probability: Relative Frequency Theoretical Probability Relative frequency can also be determined for situations involving theoretical probability. 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

10. Probability: Relative Frequency 20Black 130Silver 40White 30Green 80Blue 50Red Relative freqfreqColour 956 345 304 323 342 251 Relative freqfreqNoNo Experiment Data(Survey) Throws of a biased die. Colour of cars passing traffic lights. Worksheet 1

11. 956 345 304 323 342 251 Relative freqfreqNoNo 25/250 = 0.1 34/250 = 0.136 32/250 = 0.128 30/250 = 0.12 34/250 = 0.136 95/250 = 0.38 ColourfreqRelative freq Red50 Blue80 Green30 White40 Silver130 Black20 50/350 = 0.14 80/350 = 0.23 30/350 = 0.09 40/350 = 0.11 130/350 = 0.37 20/350 = 0.06 Worksheet 2