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PROBABILITY (Chapter 10)
221
In the late 17th century, English mathematicians compiled and analysed mortality tables.
These tables showed the number of people that died at different ages. From these tables
they could estimate the probability that a person would be alive at a future date. This led
to the establishment of the first life insurance company in 1699.
A
EXPERIMENTAL PROBABILITY
In experiments involving chance, we agree to use the following language to accurately describe
what we are doing and the results we are obtaining.
² The number of trials is the total number of times the experiment is repeated.
² The outcomes are the different results possible for one trial of the experiment.
² The frequency of a particular outcome is the number of times that this outcome is
observed.
² The relative frequency of an outcome is the frequency of that outcome expressed as a
fraction or percentage of the total number of trials.
When a small plastic cone was tossed into the air 300 times it fell on its side 203 times and
on its base 97 times. We say:
² the number of trials is 300
² the outcomes are side and base
² the frequency of side is 203 and base is 97
² the relative frequency of side =
² the relative frequency of base =
203
300
97
300
¼ 0:677
side
¼ 0:323
base
In the absence of any further data, the relative frequency of each event is our best estimate
of the probability of it occurring.
The estimated experimental probability is the relative frequency of the event.
We write Experimental P(side) ¼ 0:677, Experimental P(base) ¼ 0:323:
EXERCISE 10A
1 A coin is tossed 100 times. It falls heads 47 times. What is the experimental probability
that it falls: a heads b tails?
2 A die is rolled 300 times
and the results are:
Result
Frequency
1
52
2
47
3
50
4
51
5
49
6
51
What is the experimental probability of rolling:
a a6
b a2
c a 6 or a 2?
3 A batch of 145 paper clips was dropped
onto 6 cm by 6 cm squared paper. 113 fell
completely inside squares and 32 finished up
on the grid lines. Find, to 2 decimal places,
the estimated probability of a clip falling:
cyan
magenta
6 cm
inside
yellow
95
100
50
6 cm
75
25
0
5
95
100
50
b on a line.
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
a inside a square
on
black
Y:\HAESE\IB_MYP4\IB_MYP4_10\221IB_MYP4_10.CDR Thursday, 13 March 2008 2:31:53 PM PETERDELL
IB MYP_4