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.

number of times that the event ocRelati

curs =

numbeve

r Frequenc

of try

ials

Colour freq Relative freq

Red 50

Blue 80

Green 30

White 40

Silver 130

Black 20956

345

304

323

342

251

Relative freqfreqNo

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.

250 trials 350 trials

Probability: Relative Frequency

number of times that the event ocRelati

curs =

numbeve

r Frequenc

of try

ials

Colour freq Relative freq

Red 50

Blue 80

Green 30

White 40

Silver 130

Black 20956

345

304

323

342

251

Relative freqfreqNo

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%

Probability: Relative Frequency

number of times that the event ocRelati

curs =

numbeve

r Frequenc

of try

ials

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 freqfreqNo

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

Probability: Relative Frequency

number of times that the event ocRelati

curs =

numbeve

r Frequenc

of try

ials

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

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

40/350 = 0.11

130/350 = 0.37

20/350 = 0.06

Probability: Relative Frequency

number of times that the event ocRelati

curs =

numbeve

r Frequenc

of try

ials

Blue Green Red Yellow White

8 85 200 115 92

(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

4

1

23 4

7

6 55 8

5

37

9

9

99

9

3

Probability: Relative FrequencyTheoretical 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

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 Spins 500 Spins 720 Spins

4

1

23 4

7

6 55 8

5

37

9

9

99

9

3

Probability: Relative FrequencyTheoretical 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

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 Spins 270 Spins 560 Spins

6

6

23 6

2

2 22 8

5

37

5

7

74

8

3

Probability: Relative FrequencyTheoretical 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