Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
Mathematics
GCSE Practice
Tree Diagrams
Past Exam Questions
e.g.
A die is rolled twice. Complete a tree diagram to show the
probability of obtaining a 3
1
6
Sum of
Probabilities
=1
1
6
5
6
3
5
6
not 3
1
6
3
not 3
5
6
Find :
3
(a) Prob of obtaining two 3s
(b) Prob of obtaining one 3
not 3
Sum of Probs on
adjacent branches = 1
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
ALWAYS
Identify the route through the branches to bring about the desired
outcome.
3
1
6
1
6
5
6
3
5
6
not 3
1
6
3
not 3
5
6
not 3
Note: When moving from left to right along the branches, multiply the
Probs for each branch.
(a) Prob(Two 3s) =
1 x 1 = 1
6
6
36
N.B. Multiply fractions as follows:
Multiply tops (numerators) and multiply bottoms (denominators)
e.g.
2 x 4 = 8
3
5
15
3 x 1 =
4 2
3
8
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
(b)
If there is more than one route through the branches to bring about
the desired outcome, ADD the probs for each route together.
1
6
1
6
5
6
3
3
5
6
not 3
1
6
3
1 x 5 = 5
6
6
36
5 x 1 = 5
6
6
36
not 3
5
6
Prob(one 3) =
not 3
5 + 5 = 10
36 36
36
(or 5 )
18
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
Practice questions :
1.
At an old people’s party, the probability that Doris will win the
Bingo prize is 0.05. The probability that she will win the raffle
prize is 0.15.
a) Complete the tree diagram.
Raffle
Bingo
0.15
Doris wins
Doris wins
0.05
Doris loses
Doris wins
Doris loses
Doris loses
b)
What is the probability that Doris loses both?
c)
What is the probability that Doris wins one prize?
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
2.
The probability that a Briton is obese in 1/6. The probability that an
American is obese is 1/3. A Briton and an American are in a lift.
a.) Complete the tree diagram
American
Briton
1
/3
Obese
Obese
1
/6
Not obese
Obese
Not obese
Not obese
b.) What is the probability that
i)
ii)
both people in the lift are obese?
one person in the lift is obese?
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
3.
The probability that Jane is late for school is 1/9
The probability that John is late for school is 2/7
a.) Complete the tree diagram
John
Jane
Late
Late
Not late
Late
Not late
Not late
b.) What is the probability that
i)
both are late for school?
ii)
one of them is late for school?
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
4.
On any day, the probability that Norman oversleeps is 1/6.
The probability that his bicycle has a flat tyre is 1/9.
If either of these things happen he is late for his paper round.
a.) Complete the tree diagram.
Tyre flat
Oversleep
Not flat
Tyre flat
Not oversleep
Not flat
b.) Calculate the probability that :
i)
ii)
Norman is not late for his paper round
Norman is late for his paper round
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
5.
A bag contains 4 red beads & 3 blue beads.
A second bag contains 2 red beads & 8 blue beads.
John takes one bead at random from each bag.
a.) Complete the tree diagram.
2nd Bag
1st Bag
Red
Red
Blue
Red
Blue
Blue
b.)
Find the probability that John takes …
i.
ii.
two red beads,
one bead of each colour.
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
6.
Chesney throws two fair dice; a blue dice and a red dice.
He notes the score on each dice.
a) Complete the tree diagram to show the probabilities of
each dice showing four or not showing four.
Red
Blue
4
4
Not 4
4
Not 4
Not 4
b) Calculate the probability that Chesney gets
iii)
iv)
Two fours
One four
Cyflawni Dysgu o Ansawdd ar gyfer Plant a Phobl Ifanc yn Wrecsam
Achieving Quality Learning for Children and Young People in Wrexham
7.
Simon has a biased dice. The probability of throwing a 6 with the
dice is 0.3. Simon throws the dice twice.
a.) Complete the tree diagram
2nd Throw
1st Throw
6
6
Not 6
6
Not 6
Not 6
b)
What is the probability that Simon does not throw a six in his two
throws?
c)
What is the probability that Simon throws exactly one six in his
two throws?