The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Homework on Probability and expectation – grade C
1.
Alan, Bob and Colin play a game of darts.
There is only one winner.
The probability that Alan wins the game is 0.3
The probability that Bob wins the game is 0.5
(a)
Write down the probability that Alan does not win the game.
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Answer .........................................................................
(1)
(a)
What is the probability that Alan or Bob wins the game?
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Answer .........................................................................
(1)
(b)
Alan, Bob and Colin play 20 games of darts.
How many games would you expect Colin to win?
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Answer .........................................................................
(4)
(Total 6 marks)
2.
A game is played with a coloured spinner.
Blue
Green
Red
White
The arrow is spun once.
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
The table shows some of the probabilities of the arrow landing on a colour.
Colour
Probability
Red
0.4
Blue
0.2
Green
0.3
White
(a)
Calculate the probability that the arrow lands on red or blue.
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Answer ..........................................................................
(2)
(b)
Calculate the probability that the arrow lands on white.
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Answer ..........................................................................
(2)
(c)
The arrow is spun 250 times.
Calculate the number of times you would expect the arrow to land on red or green.
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Answer ..........................................................................
(3)
(Total 7 marks)
3.
Red, blue, white and green tickets are sold in a raffle.
The table shows some of the probabilities of these tickets winning the first prize.
Ticket colour
Probability of winning
first prize
Red
0.4
Blue
0.2
White
0.1
Green
(a)
Calculate the probability of a green ticket winning the first prize.
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Answer ........................................................................(2)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
(b)
There were 1000 tickets sold in this raffle.
Calculate how many red tickets and blue tickets were sold altogether.
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Answer ........................................................................
(2)
(Total 4 marks)
4.
A school has 1260 students.
The probability that a student at the school has blue eyes is
2
.
5
Calculate how many students at the school have blue eyes.
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Answer .........................................................................
(Total 2 marks)
5.
In a survey about favourite methods of travel people could choose car, train, coach or aeroplane.
The following probabilities were calculated from the results.
Method of travel
Probability
Car
0.45
Train
Coach
0.17
Aeroplane
0.12
200 people took part in this survey.
How many chose train?
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Answer ………………………………….........
(Total 4 marks)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
6.
A bag contains 200 coloured discs.
The discs are either red, blue or yellow.
There are 86 red discs in the bag.
The probability that a blue disc is chosen from the bag is 0.22
Calculate the number of yellow discs in the bag.
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Answer ..........................................................................
(Total 4 marks)
7
A scout group organises a game to raise money.
200 people each pay £2 to play the game.
1
The probability that a person wins is
10 .
The winners each receive £5 and there are no other prizes.
Calculate how much profit the scout group makes from this game.
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Answer £ .......................................
(Total 4 marks)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
1.
(a)
0.7
B1
(b)
(c)
0.8
1 – (0.3 + 0.5)
Or 1 – (0.8) ft their 0.8 from (b)
B1
M1
= 0.2
A1 ft
20 × “0.2”
M1
ft their 0.2
=4
A1
Accept alternative method leading to Alan 6 games & Bob 10
games and thus Colin 4 games
[6]
2.
(a)
(b)
0.4 + 0.2
M1
(=) 0.6
A1
1–(0.4 + 0.2 + 0.3)
M1
(Measure from diagram 36° 36 M1A1)
360
35
36  2
M1
360
360
(=) 0.1
(c)
A1
0.4 + 0.3
M1
oe 0.4 × 250 = (100)
or 0.3 × 250 = (75)
0.4 + 0.3 × 250 M1 no brackets
(their) 0.7 × 250
Addition 0.4 × 250 + 0.3 × 250
(=) 175
M1 dep
A1
Penalise incorrect notation 175
250
once on paper
175 out of 250 OK
[7]
3.
(a)
(b)
1 – (0.4 + 0.2 + 0.1)
M1
= 0.3
A1
(0.4 + 0.2) × 1000
Or 0.6 × 1000
M1
oe
= 600
400 and 200 misread
“400 or 200” together
A1
M1 A0
M1
[4]
4.
2
1260 ×
5
M1
= 504
A1
756
SC1
[2]
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
5.
1 – (0.45 + 0.17 + 0.12)
M1
= 0.26
A1
200 × 0.26
M1
= 52
not
52
200
or 0.45 × 200
or 0.17 × 200
or 0.12 × 200
90, 34 24
All 3 correct
200 – (90 + 34 + 24)
or 200 – 148
Alternative method
0.74 × 200
148
200 – 148
A1
[4]
6.
0.22 × 200
M1
A1ternative method
86 or = 0.43
200
M1
= 44
A1
1 – ((their) 0.43 + 0.22) = 0.35 M1
200 – ((their) 44 + 86)
(their) 0.35 × 200
M1 dep
M1
= 70
A1
= 70 Penalise incorrect notation
70 once on paper
200
A1
Do not accept extra working 70
2
[4]
7.
1/10 × 200
M1
= 20
A1
Calculating no. of winners
20 seen implies M1A1 unless clearly from incorrect working
“400” – (their “20” × 5)
= £300
M1 dep
A1
[4]
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