What is probability?



The Weather
Forecast
Winning the Super 5
or a Lottery
Arriving first in a race
Certain or Impossible?
Certain
 Sunday comes after
Saturday
 We need to eat and
drink every day
1) Sunday comes after Saturday
3) The sun will not rise tomorrow


Impossible
I win the lottery
without buying a ticket
The sun will not rise
tomorrow
2) I win the lottery without buying a ticket
4) We need to eat and drink every day
Likely or Unlikely?

Mary never does her homework and does
not study? Will she pass the exam?

John takes good care of a plant, he waters
it, gives it fertilizer etc.. Will the plant grow
and not die?
Evens
This is why coin flipping has been used as a means of solving disputes for
centuries! Coin flipping is a method that trusts the decision to pure luck, It is
generally assumed that the outcome is unpredictable, with equal probabilities
for the two outcomes. Today we often see people flip a coin at the beginning
of several sports matches, such as football.
An equal chance of something happening or not happening is called EVENS
Probability of an event
Mary passes exam if
she never does her
homework or studies
unlikely
If I take good care of a plant by
watering it, giving it fertilizer
etc.. It will grow and not die
Impossible
evens
I live without
eating or
drinking
Tossing a
coin and
getting a
head
likely
Certain
Sunday
comes after
Saturday
Spinners
link to view a virtual Spinner
Spinners
Chances of Spinning Blue
Impossible
Impossible
0
8
=
0
Certain
Very Unlikely
1
8
Equally likely
4
8
=
1
2
Very likely
7
8
Certain
8
8
= 1
Die

Dice have been used throughout Asia
since before recorded history.

The oldest know dice were excavated
at the Burnt City archaeological site in
south-eastern Iran.

In China, India, Japan, Korea and
other Asiatic countries, dice have
always been popular and are still. The
marking on Chinese dominoes evolved
from the markings on dice, taken two
at a time.
How can I never get a 1 or a 6!!
How difficult is it to get a 1 or 6 when
tossing a die?
Tossing a die
P(1) = P(2) = P(3) = P(4) = P(5) = P(6) =
P (getting a 1) =
P (getting a 2) =
1
6
1
6
P (getting a 6) =
1
6
1
6
Probability an event does NOT occur
P(not 1) = P(getting a 2,3,4,5 or 6) =
5
6
P(getting a 1) = 16
P(getting one from all possibilities) = P(getting a 1,2,3,4,5 or 6) =
P(not 1) = P(all possibilities) – P(1) =
6
1
6
6
=
5
6
So P(event does not occur) = 1 – P(event occurs)
6
6
Beads in a bag
P(picking a red bead) =
1
2
P(picking a black bead) =
P(picking a red bead) =
1
2
1
3
P(picking a black bead) =
2
3
Using a pack of cards
If a card is drawn at random from a pack of
52, find the probability that it is:
 a king

P(king) =
4
1
=
13
52
P(heart) =
13
1
=
4
52
a heart
Students’ School transport
70% of the Maltese students go to school by bus. The
other students are driven to school by their parents.
What is the probability that a student chosen at random
has been driven to school by his parents?
70% use bus = 70 out of 100 students
=> 30 out of 100 students go to school driven by parents
P(student uses family transport) =
30
100
=
3
10
Passengers on a bus
On a bus there are 48
passengers. 20 are men and
28 are women. A passenger is
chosen at random. What is the
probability that the passenger
is:


female
male
P(female) =
P(male) =
28
48
20
48
=
=
7
12
5
12
Colourful beads in a bag
A bag contains 4 pink beads, 3 blue beads and 3 green
beads. If 1 bead is drawn at random from the bag, find the
probability that the bead is:

Pink

not blue

yellow
P(pink) =
4
10
=
2
5
P(not blue) = 1 – P(blue) = 1 -
P(yellow) =
0
10
=0
3
7
=
10 10
Possibility Spaces
You own a skirt, a jeans and a pair of trousers. You also have a pink
top, a blue top and a white top. How many different combinations
can you create so that you will not look the same everyday?
On one day I can wear the

skirt + pink top

Skirt + blue top

Skirt + white top

Jeans + pink top

Jeans + blue top

Jeans + white top

Trouser + pink top

Trousers + blue top

Trousers + white top
Skirt
Jeans
Trousers
Pink top + skirt
Pink top +
jeans
Pink top +
trousers
Blue top Blue top + skirt
Blue top +
jeans
Blue top +
trousers
White top +
jeans
White top +
trousers
Pink top
White
top
White top +
skirt
The Fruit Machine
The fruit machine has 2 windows. Each
window can show a water melon,
cherries, strawberries and pineapples.
To win the game the set of fruit appearing
in the 2 windows should be the same.
What is the probability of getting a water
melon and a pineapple?
What is the probability of winning the
game?
What is the probability of not winning?
Water
melons
Cherries
Strawberri
es
pineapple
s
Water
melons
Wm & Wm Ch & Wm
St & Wm
Pin & Wm
Cherries
Wm & Ch
Ch & Ch
St & Ch
Pin & Ch
Strawberri Wm & St
es
Ch & St
St & St
Pin & St
pineapple
Ch & Pin
St & Pin
Pin & Pin
Wm & Pin
2
1
P(water melon and pineapple) = 16 = 8
4
P(winning the game) = 16 =
P(not winning) =
12
16
=
1
4
3
4
OR P(not winning) = 1 – P(winning) = 1 -
1
4
=
3
4
Tossing two dice at the same time




A game is played using two dice. The player can
play again if the number on the two dice is the
same.
Draw a possibility space illustrating all the
possible combinations when throwing two dice.
What is the probability the player obtains a 6 in
at least one of the dice?
What is the probability the player can play again
11
P(getting at least one 6) = 36
1
2
3
4
5
6
1
1,1
1,2
1,3
1,4
1,5
1,6
2
2,1
2,2
2,3
2,4
2,5
2,6
3
3,1
3,2
3,3
3,4
3,5
3,6
4
4,1
4,2
4,3
4,4
4,5
4,6
5
5,1
5,2
5,3
5,4
5,5
5,6
6
6,1
6,2
6,3
6,4
6,5
6,6
P(player plays again) =
6
36
=
1
6