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16.3 Using relative frequency

16.3 Using relative frequency

Have you ever used drawing pins to "x notices to boards?
If you drop a drawing pin it can land point up or point down. Point Point
up down
However, you cannot assume these outcomes are both equally likely.
You can estimate the probability that a drawing pin will land point up by dropping it a number of times
and "nding the relative frequency. !e more times you drop it, the better the estimate will be.
If you cannot use equally likely outcomes to work out a probability, you can use relative frequency.

Worked example 16.3
Xavier does a survey of the number of passengers in cars passing his school in the morning.

Number of passengers 1 2 3 4 5 or more
Frequency 42 28 7 12 4

Estimate the probability that the number of passengers is: a 2 b more than 2.

a The number of cars is 93. 42 + 28 + 7 + 12 + 4 = 93
The relative frequency is 28 .
93
The probability is 0.30 (2 d.p.). 28 ÷ 93 = 0.3010… It is sensible to round this to two decimal places.
23
b The relative frequency is 93 . 7 + 12 + 4 = 23
The probability is 0.25 (2 d.p.) 23 ÷ 93 = 0.2473… Give the estimated probability as a decimal.

) Exercise 16.3

1 Look again at the table in Worked example 16.3.
Estimate the probability of there being: a 1 passenger b 1 or 2 passengers.
2 Each of the faces on a cardboard cube is a different colour. Hassan throws the cube 150 times and
records the colour on the top. The results are shown in the table.
Estimate the probability of getting:
a black b red, white or blue c neither black nor white.

Score Red Blue Yellow Green White Black

Frequency 29 17 33 15 25 31

3 This table shows the heights of some plants grown from seed.
A plant is picked at random. Estimate the probability that the height will be:
a less than 5 cm b 10 cm or more.

Height (cm) 0– 5– 10– 15–20
Frequency 6 25 11 3

4 In 2009 in the UK 781 000 women gave birth. Twins means 2 babies.
12 595 had twins. 172 had triplets. Five had four or more babies. Triplets means 3 babies.
Estimate the probability of having: a twins b one baby.
16 Probability 155