The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Homework on probability tree diagrams - higher
1.
Philip and Abdul run in different races.
The probability that Philip wins his race is 0.7 The probability that Abdul wins his race is 0.6
(a)
Fill in the missing probabilities on the tree diagram.
Philip
Abdul
0.6
Win
........
Not win
0.6
Win
Win
0.7
........
Not win
........
Not win
(1)
(b)
Calculate the probability that only one of the boys wins his race.
......................................................................................................................................
......................................................................................................................................
Answer ..................................................................
(3)
(Total 4 marks)
2.
Greg has four suits, one is striped and the other three are plain.
He also has ten shirts, four are white and the other six are coloured.
Greg chooses a suit at random and then chooses a shirt at random.
(a)
Fill in the probabilities on the branches of the tree diagram.
SUIT
SHIRT
White
Striped
Coloured
White
Plain
Coloured
(3)
(b)
Calculate the probability that Greg chooses a plain suit and a coloured shirt.
......................................................................................................................................
Answer ..........................................
(2)
(Total 5 marks)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
3.
Danny has a biased coin.
The probability that the coin lands heads is
2
.
3
Danny throws the coin twice.
(a)
Fill in the probabilities on the tree diagram.
First throw
Second throw
Head
...............
Head
...............
...............
Tail
Head
...............
...............
Tail
...............
Tail
(2)
(b)
Calculate the probability that Danny gets two heads.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ...................................................................................
(2)
(Total 4 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
4.
Jean enters an archery competition.
If it is raining the probability that she hits the target is 0.4.
If it is not raining the probability that she hits the target is 0.7
The probability that it rains on the day of the competition is 0.2
(a)
Draw a fully labelled tree diagram showing all the probabilities.
(3)
(b)
Calculate the probability that Jean hits the target with her first arrow in the competition.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ...............................................................
(3)
(Total 6 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
5.
Shereen has two bags of marbles.
Bag A contains 3 red marbles and 4 green marbles.
Bag B contains 2 red marbles and 3 green marbles.
Shereen throws a fair six-sided dice.
If the dice lands on a six, she takes a marble at random from bag A.
If the dice lands on any other number, she takes a marble at random from bag B.
(a)
Draw a fully labelled tree diagram showing the above information.
Mark the probabilities on the appropriate branches.
(3)
(b)
Calculate the probability that a red marble is selected.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer ..................................................................
(3)
(Total 6 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
1.
(a)
All 3 missing probabilities correctly filled in
B1
(b)
0.7 × 0.4 or 0.6 × 0.3
ft from unambiguous tree diagram except if 0.5 used
Either seen in (b) or 0.28 or 0.18
M1
“0.28” + “0.18”
Adding the 2 “correct” products
If no working in (b) answer can follow tree diagram if fully
correct to answer in (b)  M1 M1
* Working in (b) can be ft from incorrect tree diagram as long
as it is not ambiguous ( M1M1A0)
M1
= 0.46
A1
[4]
2.
(a)
Any one correct probability seen
Seen anywhere in (a)
M1
1
3
and correctly placed
4
4
Or 0.25, 0.75
(b)
A1
4
6
and correctly placed
10
10
twice
Or 0.4, 0.6 (twice)
A1
3 6

4 10
M1
ft their tree if possible (unambiguous)

9
(or 0.45)
20
oe
A1
[5]
3.
(a)
(b)
2
1
and on first pair of branches
3
3
Remainder fully correct
B1
B1
2 2

3 3
M1
0.66 × 0.66 or 0.67 × 0.67
=
4
or 0.44 or better
9
= 0.43 A0
A1
= 0.44 A1
= 0.42 A0
[4]
4.
(a)
1st branches label(s) and probs correct
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B1
5
The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Must have 1 label and both probs correct
2nd branches label(s) and probs correct
B1 B1
st
B1 each set. Must follow from 1 set of branch labels correctly
(b)
0.2 × 0.4 or 0.8 × 0.7
Any correct product (not ft)
M1
0.2 × 0.4 + 0.8 × 0.7
Adding the correct products
M1
= 0.64
A1
0.8 + 0.56 = 0.64  M1M1A0
[6]
5.
Note: Probability - Accept fraction, decimal or percentage. Do not accept ratio.
eg 1 out of 3 or 1 in 3 penalise once on whole paper.
(a)
First set of branches correctly labelled with 6/not 6 and correct probabilities
Or Bag A and Bag B labels as long as unambiguous or 2nd
labels in outcome columns
B1
Second set - Bag A has probs
red
3
4
, green
B1 dep
7
7
Condone omission of labelling of bags if there is no ambiguity
Must have R, G labels
Second set - Bag B has probs
red
(b)
2
3
, green
5
5
Dependent upon correct true diagram structure
<
<
<
1 3
5 2
 and 
6 7
6 5
oe ft if clearly unambiguous from correct structured tree
diagram
“
1
1
”+“ ”
3
14
oe ft if clearly unambiguous from correct structured tree
diagram
17
42
B1 dep
M1
M1
A1
Accept
51
126
[6]
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