PROBABILITY

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PROBABILITY
TREE DIAGRAMS Part 1 Drawing
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A tree diagram is a way of describing all the
possible outcomes from a series of events
A tree diagram is a way of calculating the
probability of all the possible outcomes from a
series of events
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A list of possible events could include

• Picking a square on a chess board

Black or white
Head or tail

• Flipping a coin

• Taking a sweet from a jar of red, yellow and
  green sweets

What is different about the outcome here?
There are 3 outcomes
Red, yellow or green
All these events have definite outcomes
CLICK
CLICK
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Each event can be represented by a tree diagram
Picking a sweet from a jar containing red, yellow
and green sweets
Picking a square on a chess board
Flipping a coin
BLACK
REMEMBER there are 3 outcomes
HEAD
RED
WHITE
TAIL
YELLOW
The diagram shows you have a choice of 2 paths
(branches)
The diagram shows you have a choice of 2 paths
(branches)
GREEN
The diagram shows you have a choice of 3 paths
(branches)
CLICK
CLICK
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THE TREE DIAGRAM IS NOT COMPLETE
WE NEED THE PROBABILITIES ADDING
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The list of possible events and their outcomes are
Probability of black 0.5 Probability of white
0.5

• Picking a square on a chess board

Black or white
Equal number of black and white squares Therefore
the probability of each outcome is 0.5
Probability of head 0.5 Probability of tail
0.5
Equal chance of head or tails Therefore the
probability of each outcome is 0.5

• Flipping a coin

Head or tail
The remaining event needs more investigation

• Picking a sweet from a jar of red, yellow and
  green sweets

Red, yellow or green
All these outcomes have definite probabilities
CLICK
CLICK
CLICK
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EVENT Picking a sweet from a jar of coloured
sweets
In the jar there are 12 red sweets 5 yellow
sweets 8 green sweets
0.48
Probability of picking a red is
12 out of 25
Probability of picking a yellow is
0.20
Probability of picking a green is
0.32
CLICK
CLICK
CLICK
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CLICK
The tree diagrams can now be completed
Picking a square on a chess board
So far we have the outcomes drawn

BLACK
0.5
0.5
0.5
WHITE
0.5
0.5
0.5
Now we add the probabilities
Probability of BLACK 0.5
Probability of WHITE 0.5
THE TREE DIAGRAM IS NOW COMPLETE
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Similarly, the tree diagram for flipping a coin is
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Picking a sweet from a jar of red,yellow and
green sweets
Probability of RED 0.48
RED
0.48
Probability of yellow 0.2
0.2
YELLOW
0.32
GREEN
Probability of GREEN 0.32
These are the outcomes
The tree diagram is compete
We must add the probabilities
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What do we do if there are 2 events?
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A coin is flipped twice
The second flip may be HEAD
The first flip may be HEAD
OR the second flip may be TAIL
OR the first flip may be TAIL
OUTCOME
HEAD
H
H
0.5
HEAD
0.5
TAIL
H
T
0.5
HEAD
T
H
0.5
TAIL
0.5
T
T
TAIL
0.5
THE COMPLETED TREE DIAGRAM SHOWS THERE ARE 4
POSSIBLE OUTCOMES
CLICK
CLICK
CLICK
CLICK
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Click on your choice
Re-start Drawing Tree Diagrams