Download Probability: Higher

Which grade are you…..?
Probability: Higher
Time
Less than 5 minutes
More than 5 minutes but less than 10 minutes
More than 10 minutes
Number of patients
17
18
5
a) What is the probability that a patient chosen at random will wait more than 10
minutes?
Grade D
1 A doctor surgery keeps a record of how long patients wait before their appointment.
b) During a week 240 patients have appointments. How many would you expect have to
wait more than 5 but less than 10 minutes?
Orange
Water
0.15
Tropical
0.25
Lemon
Other
0.2
A student is three times as likely to pick orange than lemon.
Grade C
2 The table shows the probabilities that a student will chose a certain drink
a) What is the probability that a student chooses Orange?
b) What is the probability that the student doesn’t choose Tropical?
c) What is the probability that the student chooses Tropical or Lemon?
3 Two dice are rolled and the ‘score’ is the difference between the numbers shown.
a) Copy and complete the sample space to show all possible outcomes
1
2
0
1
2
3
4
5
6
4
0
3
Grade C
1
0
4
2
5
6
5
4 The probability that Matt cycles to work is 0.4.
The events are independent of each other.
What is the probability that Matt cycles to work on Tuesday and Wednesday?
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Grade B/A
b) What is the probability of getting a score of 3?
c) What is the probability of the score being an odd number?
What is the probability that she takes
a) an apple and orange juice
b) an apple but not orange juice
c) neither an apple or orange juice?
Grade A
5 Kate takes fruit and a drink to work each day.
The probability that she takes an apple is 0.6
The probability that she takes orange juice is 0.45
Use a tree diagram to find the probability that
Grade A
6 37% of the UK population go abroad for their annual holiday.
Two people are chosen at random.
7 A bag contains 80 discs coloured in the ratio 3 : 5
Two discs are drawn at random (without replacement)
Use a tree diagram to find the probability that a disc of each colour is selected.
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Grade A*
a) both of them go abroad for their holiday.
b) at least one of the them goes abroad for their holiday.
Which grade are you…..?
ANSWERS
Probability: Higher
Time
Less than 5 minutes
More than 5 minutes but less than 10 minutes
More than 10 minutes
Number of patients
17
18
5
a) What is the probability that a patient chosen at random will wait more than 10
minutes? 
Grade D
1 A doctor surgery keeps a record of how long patients wait before their appointment.
b) During a week 240 patients have appointments. How many would you expect have to
wait more than 5 but less than 10 minutes? 108 
Orange
Water
0.15
Tropical
0.25
Lemon
Other
0.2
A student is three times as likely to pick orange than lemon.
Grade C
2 The table shows the probabilities that a student will chose a certain drink
a) What is the probability that a student chooses Orange? 0.3 
b) What is the probability that the student doesn’t choose Tropical? 0.75 
c) What is the probability that the student chooses Tropical or Lemon? 0.35 
1
2
1
0
1
2
0
2
1
1
0
2
5
1
2
3
4
6
5
1
2
3
3
4
3
4
3
4
5
6
3
2
1
0
1
2
4
5
4
3
2
1
0
3
2
1
0
1
Grade C
3 Two dice are rolled and the ‘score’ is the difference between the numbers shown.
a) Copy and complete the sample space to show all possible outcomes
b) What is the probability of getting a score of 3?

c) What is the probability of the score being an odd number? 
www.mathsbox.org.uk
Grade A
5 Kate takes fruit and a drink to work each day.
The probability that she takes an apple is 0.6
The probability that she takes orange juice is 0.45
Grade B/A
4 The probability that Matt cycles to work is 0.4.
The events are independent of each other.
What is the probability that Matt cycles to work on Tuesday and Wednesday? 0.16 
What is the probability that she takes
a) an apple and orange juice 0.27 
b) an apple but not orange juice 0.33 
c) neither an apple or orange juice? 0.22
Grade A
6 37% of the UK population go abroad for their annual holiday.
Two people are chosen at random.
Use a tree diagram to find the probability that
7 A bag contains 80 discs coloured in the ratio 3 : 5
Two discs are drawn at random (without replacement)
Use a tree diagram to find the probability that a disc of each colour is selected.
0.4747 
25 marks
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Grade A*
a) both of them go abroad for their holiday 0.1369 
b) at least one of the them goes abroad for their holiday 0.6031 