Transcript Scratch cards

Probability
The probability scale
The chance of an event happening can be shown on a
probability scale.
The sun
won’t rise
tomorrow
A day of the
week starting
with a T
The next baby
born being a
girl
You will
receive a
text today
A square
having four
right angles
impossible
unlikely
even chance
likely
certain
Less likely
More likely
The probability scale
We measure probability on a scale from 0 to 1.
If an event is impossible or has no probability of occurring
then it has a probability of 0.
If an event is certain it has a probability of 1.
This can be shown on the probability scale as:
0
impossible
1
2
even chance
1
certain
Probabilities are written as fractions, decimals and, less
often, as percentages between 0 and 1.
Listing possible outcomes
When you roll a fair dice you are equally likely to get one
of six possible outcomes:
1
6
1
6
1
6
1
6
1
6
1
6
Since each number on the dice is equally likely the
probability of getting any one of the numbers is 1 divided
1
by 6 or
.
6
Calculating probability
If the outcomes of an event are equally likely then we can
calculate the probability using the formula:
Probability of an event =
Number of successful outcomes
Total number of possible outcomes
For example, a bag contains 1 yellow,
3 green, 4 blue and 2 red marbles.
What is the probability of pulling a green
marble from the bag without looking?
P(green) =
3
10
or 0.3 or 30%
Calculating probability
What is the probability of the following events?
1) A coin landing tails up?
P(tails) = 1
2
2) This spinner stopping on
the red section?
1
P(red) =
4
3) Drawing a seven of hearts
from a pack of 52 cards?
P(7 of
)=
1
52
4) Your birthday being on a
Friday this year?
P(Friday) =
1
7
Scratch cards
Scratch off a $ sign
and win $100!
£
no
win
£
no
win
no
win
no
win
no
win
£
no
win
no
win
$
$
no no
win win
no no
win win
$
no no no no
win win win win
no no
win win
$
no
win
no no no no
win win win win
no
win
$ $
no
win
$
no no
win win
$
You are only allowed to scratch off one square and you can’t
see what is behind any of the squares.
Which of the scratch cards is most likely to win a prize?
Calculating probability
A fair dice is thrown. What is the probability of getting
a) a 2?
b) a multiple of 3?
c) an odd number?
d) a prime number?
e) a number bigger than 6?
f) an integer?
a) P(2) = 1
6
2
1
b) P(a multiple of 3) =
=
6
3
3
1
c) P(an odd number) =
=
6
2
Calculating probability
A fair dice is thrown. What is the probability of getting
a) a 2?
b) a multiple of 3?
c) an odd number?
d) a prime number?
e) a number bigger than 6?
f) an integer?
d) P(a prime number) =
3
1
=
6
2
e) P(a number bigger than 6) = 0
6
f) P(an integer) =
6
= 1
Don’t write
0
6
Probability
Exercise 8.1 – Page 246