Transcript Probability Tree diagrams - thomas whitham maths site

Probability Tree diagrams
Example
A coin is tossed twice. Complete the probability tree diagram
showing all the possible outcomes and the probability of each.
What is the probability of the two tosses giving the same result?
1st throw
1
2
1
2
2nd throw
1
2
Head
1
2
Tail
1
2
1
2
Head
Head, Head
Tail
Head, Tail
Head
Tail, Head
Tail
Tail, Tail
Example
A six sided dice is thrown twice. Complete the tree
diagram showing all the probabilities
1st throw
1
6
5
6
2nd throw
1
6
four
5
6
Not 4
1
6
5
6
four
Not four
Four
Not four
What is the probability of throwing a total of
(a) two fours?
(b)No fours?
(c) At least one four?
four, four
four, Not four
Not four, four
Not four, Not four
Example
It is found that the probability of a particular brand of firework will
not light is
.
John buys two. Copy and complete the tree diagram and use it to
find the probability that both of his fireworks light.
First Firework
second Firework
Lights
Lights
Fails
Lights
Fails
Fails
Example
When cultivating fruit bushes by planting cuttings the probability that
a cutting produces a bush is 3/5. Find the probabilities of 0, 1, 2
bushes being produced, if two cuttings are planted.
1st cutting
3
5
2
5
2nd cutting
3
5
Bush
2
5
No
Bush
3
5
2
5
Bush
Bush, Bush
No
Bush
Bush, No
Bush
Bush
No Bush, Bush
No
Bush
No Bush, No Bush
Example
A box contains seven red and three blue pens. Jane takes a pen
from the box and keeps it; then Susan takes a pen from the
box. Both girls make their selection without looking at the
colour.
a) Draw a tree diagram to show the possible colours each has
selected.
b) Use your tree diagram to find the probability that Jane and
Susan
(i) each select a red pen
(ii) select pens of the same colour.