Probability
Learning Outcomes
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I can find the probability of simple events, combined events and
use expectation
I can use the addition rule for Mutually exclusive events
I can understand Independent events and determine the
probability of 2 independent events occurring

I can use a probability tree to illustrate events

I can understand Dependent events
Probability
Probability
Probability is how likely an event is to happen
P(event) = No. of desired outcomes
total No. of outcomes
Example:
A dice is thrown.
The probability of getting a 3:
P(3) =
The probability of an even number P(even) =
Probability
Combined Events
Sample space ( A probability space diagram)
Example
Two dice are rolled and the numbers on each dice are added
i) Complete the probability space diagram below
ii) Find a) P(total = 6)
First die
b) P(total is even)
1
2
3
4
c) P(total ≥ 8)
Second die
1
2
3
4
5
6
5
6
Probability
Mutually Exclusive Events
Head and Tail are mutually exclusive events when a coin is tossed
Mutually exclusive – one or other of the events happen, not both.
Keyword is ‘OR’
Example
not getting
Rolling a die
- 6 OR not 6:
(6)  (6)
=1
Getting a red card
- red OR not red:
(R)  (R) = 1
Being sunny today
- sun OR no sun:
(S )  (S ) = 1
P(event) = 1 – P( event)
Probability
Mutually Exclusive Events
Example
1) Rolling a die
P(5 or 6) =
2) Probability of not raining in June given P(rain) = 0.3
P( rain ) =
Independent Events
Probability
Events are unrelated
Keyword is ‘AND’
P(A and B) = P(A) x P(B)
P(Rain on a given day) = 0.3
P(Tuesday) = 1/7
P(Rain and Tuesday) =
A coin is tossed and a die is rolled. Find:
P(Head and 6) =
Tree Diagrams
Probability
1. A bag has 5 green balls and 4 red balls. Two balls are
selected at random with replacement.
i. List the 4 possible outcomes
ii. Find P(2 red)
iii. P(1 of each colour)
iv. P(2 green)
P(2 Red) =
P(G) = 5/9
P(G) = 5/9
P(R) =
4/
9
G
P(1 of each colour) =
G
P(R) = 4/9
R
P(G) = 5/9
G
R
P(2 green) =
P(R) = 4/9
R
Tree Diagrams
Probability
1. A bag has 5 green balls and 4 red balls. Two balls are
selected at random without replacement.
i. List the 4 possible outcomes
ii. Find P(2 red)
iii. P(1 of each colour)
iv. P(2 green)
G
G
R
G
R
R
Tree Diagrams that lead to
quadratic equations
Probability
When a piece of toast is dropped it is more likely to land buttered side down.
When it is dropped twice the probability that it will only land once buttered side
down is 0.48.
What is the probability that it will land buttered side down after it is dropped
only once?
P(B) Buttered side down
P(B) Buttered side up
B
B
B
B
B
B
Probability
Additional Notes
Probability
Learning Outcomes:
At the end of the topic I will be able to
Can
Do
Revise
Further
I can find the probability of simple events, combined
events and use expectation


I can use the addition rule for Mutually exclusive
events


I can understand Independent events and determine
the probability of 2 independent events occurring



I can use a probability tree to illustrate events



I can understand Dependent events
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
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