Page 154 - Mathematics Coursebook

16.1 The probability scale

16.1 The probability scale

Words such as likely, unlikely and certain are used to describe the chance that something will happen.
Sometimes a result can be associated with a number from 0 to 1.

!is is the probability of the result. Probabilities can be written as
fractions, decimals or percentages.
t Something that is certain to happen has probability 1.
t Something that is impossible has probability 0.
Probabilities can be shown on a probability scale, as worked example 16.1 shows.

Worked example 16.1
United and City are two football teams. The probability that City will win their next match is 25%.

The probability that United will win their next match is 2 .
3
a Which team is more likely to win their next match?
b Show the probabilities on a probability scale.

a United is more likely to win their next match. 25% is 1 , which is less than 2 .
4 3
It helps to
b City United The scale goes from 0 to 1. mark a few
1
Mark 4 and 2 on the scale. fractions on the
3
probablity scale.
0 1 / 4 1 / 3 1 / 2 2 / 3 3 / 4 1

) Exercise 16.1

1 Choose the best word or phrase from the box to describe each situation.
a If you drop a fair coin it will land showing ‘heads’. E PLURIBUS likely unlikely impossible
E PLURIBUS
UNUM
UNUM
UNITED ST A TES OF AMERICA very likely very unlikely
UNITED ST A TES OF AMERICA
b The day after Monday will be Tuesday.
GOD
IR IR IR IR IR IR IR IR IR IR IRGODWE WE WE WE WE WE WE WE WE WE WE
GOD
GOD
GOD
IRGODWE
GOD
GOD
GOD
GOD
GOD
GOD
TR TR TR TR TR TR TR TR TR TRUST UST UST UST UST UST UST UST UST UST UST QUARTER DOLLAR R even chance certain
TR
TRUST
c You have the same birthday as the President of 1 9 3 3 3
QUARTER DOLLA
1 9 3 2 2 2
B
A
the United States. heads tails C D E F G
d You will do well in your next maths exam.
0
2 Match each statement to the most appropriate letter on the probability scale. 1
E PLURIBUS
E PLURIBUS
UNUM
UNUM
a A new-born baby will be a girl. UNITED ST A TES OF AMERICA
UNITED ST A TES OF AMERICA
IRGODWE
IRGODWE QUARTER DOLLAR R
b A plane will fly from New York 1 9 3 2 QUARTER DOLLA

TRUST
TRUST
to Hong Kong in two hours next week. A A A A B B B B C D E F G
c A dice will show a 2 when it is rolled.
d There will be an earthquake in Asia in
the coming year. 0 1
3 Draw a probability scale. Mark these probabilities in the correct places on your diagram.
a It will rain tomorrow: 25%. b A hurricane will reach a town: 50%.
1

c Your team will win the match: . d A plant will flower: 70%.
5
e Mia will study maths at university: 0.9. f Razi’s train will be late: 5%.
16 Probability 153