Tree Diagrams
M O N D AY, 2 4 J U N E 2 0 1 3
Example
The probability that it will rain on Monday is 0.2.
The probability it will rain on Tuesday is 0.3.
a) What is the probability that it will rain on Monday
and Tuesday?
b) What is the probability that it only rains on one
day?
Tuesday a tree diagram.
We can solve this problem by drawing
Monday
0.3
It rains
0.7
It does not rain
It rains
0.2
Now let’s look at
Tuesday
0.8
It does
not
rain
We now have the
required Tree Diagram.
It rains
0.3
What is the probability?
1 – 0.2 = 0.8
0.7
It does not rain
We wanted to know the probability that it rained on Monday and Tuesday.
Tuesday
It rains 0.2 x 0.3 = 0.06
0.3
Monday
It rains
0.2
0.8
It
does
not
rain
0.7
It does not rain
0.3
It rains
0.7
It does not rain
We
work
out the
probability
both
events
happening
multiplying
the
This
So can
the
is the
probability
only
path
that
through
it rainsof
the
on
tree
Monday
whichand
gives
Tuesday
us by
rain
is on
0.06
both days
individual probabilities together
b) Rains on only one day
Tuesday
Monday
0.3
It rains
0.7
It does not rain
0.2 x 0.7 = 0.14
0.3
It rains
It rains
0.2
0.8
It
does
not
rain
0.7
b) Rains on only one day = 0.14 + 0.24 = 0.38
0.8 x 0.3 = 0.24
It does not rain
Let’s look at the completed tree diagram
Tuesday
Monday
0.3
It rains
0.06
0.7
It does not rain
0.14
0.3
It rains
0.24
It does not rain
0.56
It rains
0.2
0.8
It does not rain
0.7
The end probabilities add up to 1. Remember this!
do you
ItWhat
can help
younotice?
check your answer!
1. There are 2 sets of traffic lights on a journey. A car
approaches the first set where the probability of stopping is
0.7. The car then gets to the second set where the probability
of stopping is 0.4.
a)
b)
Draw a tree diagram
Find the probability of:
i.
ii.
Stopping at both sets of lights.
Only stopping at one set.
2. Julie and Pat are going to the cinema. The probability that
Julie will arrive late is 0.2. The probability that Pat will arrive
late is 0.6. The two events are independent.
a)
b)
Draw the tree diagram for this data
Find the probability that:
i.
ii.
both will arrive late.
neither will arrive late.
Example
A politician can get to the house of commons by either bus,
taxi or the underground tube. If the probability of going by
bus is 0.1 and being late is 0.7, by taxi 0.6 and being late is
0.4 and by the tube 0.3 and being late is 0.5.
Draw a tree diagram
b) Find the probability of:
a)
i.
ii.
The politician being late on any given day?
Given that the politician was late he went by taxi?
Late
0.7
0.1 x 0.7 = 0.07
0.1
On time
Bus
Late
Taxi
0.3
0.4
0.6 x 0.4 = 0.24
0.6
On time
Tube
Late
0.6
0.5
0.3
On time
0.5
0.3 x 0.5 = 0.15
b) i) The politician being late on any given day?
= 0.07 + 0.24 + 0.15
= 0.46
b) ii) Given that the politician is late he went by taxi?
0.24 12
Plate and taxi 



0.46 23
Plate