2. What are Tree Diagrams
A way of showing the possibilities of
two or more events
Simple diagram we use to calculate the
probabilities of two or more events
3. For example – a fair coin is flipped twice
H
H
H
T
T
T
HH
HT
TH
TT
2nd
1st
Possible
Outcomes
4. Outcome Table
if you flip a coin twice, you can model also
model the results with an outcome table
Flip 1 Flip 2 Simple
Event
H H HH
H T HT
T H TH
T T TT
5. Tree Diagrams – For flipping a coin
Probability of two or more events
1st
Throw 2nd
Throw
THHHHH TTTT 1/21/21/21/21/21/21/2
OUTCOMES
H,H
H,T
T,H
T,T
P(Outcome)
P(H,H) =1/4=1/2x1/2
P(H,T) =1/4=1/2x1/2
P(T,H) =1/4=1/2x1/2
P(T,T) =1/4=1/2x1/2
Total P(all outcomes) = 1
Total=4 (2x2)Total=4 (2x2)
6. Multiplicative Principle for
Probability of Independent Events
if two events are independent the
probability of both occurring is…
P(A and B) = P(A) · P(B)
or P(A ∩ B) = P(A) · P(B)
INDEPENDENT EVENTS
two events are independent of each other if an
occurrence in one event does not change the
probability of an occurrence in the other
if this is not true, then the events are dependent
7. Example – 10 coloured beads in a bag – 3 Red, 2 Blue, 5
Green. One taken, colour noted, returned to bag, then a
second taken. Draw tree diagram for 2 draws.
B
RR
2nd
1st
B
B
B
R
R
R
R
G
G
G
G
RB
RG
BR
BB
BG
GR
GB
GG
Now add in theNow add in the
probabilityprobability
9. The probability of a biased coin landing
Heads up is 0.9. It is tossed twice. Draw
tree diagram and hence answer the
following. A) What is the probability of
getting Tails twice? B) What is the
probability of not getting Tails twice?
Your turn
10. A hat contains 8 purple and 2 green discs.
Two discs are selected, with replacement,
from the hat. Draw a tree diagram to
represent this situation and answer the
following questions
(i) they are both green
(ii) the first is purple and the second is green
(iii) they are identical in colour
Try this!!!!!
