Page 155 - Mathematics Coursebook

16.2 Equally likely outcomes

16.2 Equally likely outcomes

For some simple activities or events, such as spinning a coin, throwing a dice or picking a card from a
pack, there are various results, or outcomes, that are all equally likely. With a coin the two outcomes are
‘heads’ and ‘tails’. With a dice the numbers 1, 2, 3, 4, 5 and 6 are all equally likely outcomes.
But how can you assign a probability to a particular outcome?

Worked example 16.2
Here are eight number cards. 2 5 5 8 10 10 10 13 If the card is chosen at

The cards are placed face-down on a table. One card is chosen at random. random it means that all
What is the probability that the number chosen is: the cards have the same
a 5 b greater than 9 c an even number? chance of being chosen.

a 2 = 1 There are eight cards, so there are eight equally likely outcomes.
8 4
Two of the cards are 5s so there are two chances out of eight of choosing a 5.
Write this as a fraction.
4 1
b = There are four cards with numbers greater than 9.
8 2

c 5 The even numbers are 2, 8 and 10. Five cards have even numbers so the probability is 5 .
8 8

) Exercise 16.2

1 There are 20 picture cards in a set. Six show flowers, four show trees, three show birds, five show
antelopes and two show lions.
Bryn picks a card at random. What is the probability that it is:
a a bird b a lion c a plant d an animal with four legs?
2 Alicia throws a dice. What is the probability that she scores:
a 4 b more than 4 c less than 4 d an odd number?
3 There are six girls and ten boys in a class. Three of the girls and four of the boys wear glasses.
a The teacher chooses one person at random. What is the probability that the teacher chooses:
i a girl ii a girl wearing glasses
iii a boy who does not wear glasses iv a child wearing glasses?
b How can the teacher make sure that the choice is random and each child has an equal chance of
being chosen?
4 Each letter of the word MATHEMATICS is written on a separate card.
The vowels are A, E, I, O
M A T H E M A T I C S and U.
Jake picks one card at random. What is the probability that the letter is:
H E
a M b not T c a vowel d not a vowel C A N C
e X f in the word CHANCE?

154 16 Probability