Download Year 10 Probability

Year 10 Probability
Introduction to Probability
Events
Outcome
Calculations
Probability
Events:
In the language of probability, something that could or has
happened is called an event. The following are all events:
1. A mother giving birth to a baby girl.
2. Getting a 6 when you throw a die.
3. Being born in March.
4. Winning the Powerball Jackpot.
5. Leaves falling off the trees in autumn.
6. Getting a 4 when you spin the pointer.
5 4
6 2
3
Probability
6
Events:
If itprobability
is impossible
anevents
event to
happen then
it is given
a value
The
of for
most
happening
lie between
these
two of 0
on the start
the probability
line.
an event
is certain
extremes
andofcould
be described
asIf
having
an even
chance,toa happen
poor
a value
of 1 at the end of the probability line.
chance
or given
a good
chance.
5then
4 it is
40
5 4
6
4
4
4
Impossible
poor chance
even chance
good chance
1
Certain
Describe the probability of each of the following events happening.
1. A mother giving birth to a baby girl.
2. Getting a 4 on the spinner.
3. Getting a 7 on the spinner .
4. Leaves falling off trees in autumn.
5. Getting a 6 on the die.
6. Winning the Powerball Jackpot.
5 4
6
4
4
Probability
Outcomes
The probability of an event happening can be located accurately
on the probability line if we know all of the possible outcomes
that can occur.
Listing Outcomes:
Make a list of all possible outcomes for the following events. The
outcomes for these events are equally likely.
1. Throwing a die.
2. Tossing a coin.
1, 2, 3, 4, 5, 6
Head, Tail
Six outcomes
Two outcomes
3. Spinning the pointer.
Blue, red, yellow, green, white
Five outcomes
Probability
Outcomes
The probability of an event happening can be located accurately
on the probability line if we know all of the possible outcomes
that can occur.
Listing Outcomes:
How many possible outcomes are there when you choose a card
from a pack?
52
?
outcomes
Probability
The probability of an event happening =
number of wanted outcomes
total number of outcomes
Where would you place the following events on the probability line?
3
2
4
0
½
5
1
6
1
Certain
Impossible
1 Getting a tail when
tossing a coin.
1
2
2 Getting a 3 when you
throw a die.
1
6
4 Choosing a red cube at 5 Getting a 5 on the
random from the bag.
spinner.
5
12
5
4
5
5
3 9

4 12
3
Being born in the
month of March.
1
12
6
Choosing a blue bead at
random from the bag.
11
12
Remember: The probability of an event happening =
number of wanted outcomes
total number of outcomes
Discuss the probabilities of the following events and their placement on
the probability line.
6
5
½
0
1
4
2
3
1
Certain
Impossible
1 Not getting a tail
when tossing a coin.
2 Not getting a 3 when
you throw a die.
3
11
12
5
6
1
2
4 Not choosing a red
cube at random from
the bag.
7
12
5 Not getting a 5
on the spinner.
5
4
5
5
1
4
Not being born in the
month of March.
6
Not choosing a blue
bead at random from
the bag.
1
12
From what we have done below it should be clear that:
The probability of an event not happening = 1 - probability of it happening
If we call the event “A” then symbolically we
have:
P(not A) = 1 - P(A)
6
5
½
0
1
P(A’) = 1 - P(A)
4
2
3
1
Certain
Impossible
1 Not getting a tail
when tossing a coin.
2 Not getting a 3 when
you throw a die.
3
11
12
5
6
1
2
4 Not choosing a red
cube at random from
the bag.
7
12
5 Not getting a 5
on the spinner.
5
4
5
5
1
4
Not being born in the
month of March.
6
Not choosing a blue
bead at random from
the bag.
1
12
The probability of an event not happening = 1 - probability of it happening
P(not A) = 1 - P(A)
(c)
0
(a)
(b)
(f)
(e)
(d)
½
1
Jenny has 12 cards with
different shapes on as shown.
She turns the cards over and
chooses one at random. Mark
the probabilities for the chosen
card on your number line.
(a) P(red shape)
5/12
(b) P(not red shape)
7/12
(c) P(3D shape)
2/12 = 1/6
(d) P(not 3D shape)
10/12=5/6
(e) P(not triangular shape)
9/12=3/4
(f) P(not quadrilateral shape)
8/12=2/3
The probability of an event not happening = 1 - probability of it happening
P(not A) = 1 - P(A)
(d)
(c)
(a)
(e)
½
0
(b)
(f)
3
15
17
7
24
12
1
Sam has 6 cards with different
numbers on as shown. He
turns the cards over and
chooses one at random. Mark
the probabilities for the chosen
card on your number line.
(a) P(not even)
4/6 =2/3
(b) P(not prime)
3/6 =1/2
(c) P(not a multiple of 3)
2/6 = 1/3
(d) P(not less than 18)
1/6
(e) P(not greater than 20)
5/6
(f) P(not less than 7 factors)
1/6
Example:
Let  = {the numbers from 1 to 12}
Let E = {the even numbers}
Let O = {the odd numbers}
Let P = {the prime numbers}
 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
E = {2, 4, 6, 8, 10, 12}
O = {1, 3, 5, 7, 9, 11}
P = {2, 3, 5, 7, 11}
(a) List the elements of , E, O and P.
(b) Hence find the probability that a randomly selected
number is:
i. Even
ii Prime
𝟔
𝟏
𝟓
=
𝟏𝟐 𝟐
𝟏𝟐
iii. Odd
iv An even prime
𝟏
𝟔
𝟏
=
𝟏𝟐
𝟏𝟐 𝟐
v. Even and not prime 𝟓
𝟏𝟐
Exercise 8A
Proficiency/Enrichment
Understanding
Fluency
Problem-solving
Reasoning
Enrichment
Foundation
1-2
3, 5, 6
8, 9
12
—
Standard
2
7
9, 10
13, 14
—
Advanced
—
-
15