Exam code: 1350
John takes part in a Go Kart race every Saturday.
The probability that he finishes a race is 0.8
If he finishes a race the probability that he wins is 0.5 For each race there is an entry fee of £50
For each race there is a prize of £500 for the winner.
John enters 20 races.
How much money should he win?
You must show your working to justify your answer.
Was this exam question helpful?
Your blood has none, some or all of three substances: A, B and Rh.
The Venn diagram shows the percentages of people in a population whose blood has different combinations of these substances.
What is the probability that a person whose blood contains substance B also contains substance A?
David’s blood contains substances A and B but not Rh.
For Sarah to be able to donate her blood to David, any substance found in her blood must also be in David’s blood.
What is the probability that Sarah can donate her blood to David?
Was this exam question helpful?
A survey asked 250 households if they own a laptop and if they have access to full fibre broadband. The table shows the results.
Full fibre broadband | |||
Yes | No | ||
Laptop | Yes | 64 | 82 |
No | 42 | 62 | |
One household included in the survey owns a laptop.
Work out the probability the household does not have access to full fibre broadband
In the UK, 12.4 million households have access to full fibre broadband.
Use the information in the table to estimate the number of households in the UK that own a laptop.
Give one reason why your answer to question 4 (b) might not be a good estimate.
Was this exam question helpful?
In a town there are two secondary schools, Audley Academy and Banford School.
At Audley Academy
there are 120 students in Year 10
all students study either history or geography.
The Venn diagram shows the number of students in Year 10 that study each subject at Audley Academy.
Two students in Year 10 at Audley Academy are chosen at random.
Work out the probability that one studies history and one studies geography.
At Banford School
there are 180 students in Year 10
8 students in Year 10 study both history and geography 50 students in Year 10 study neither history nor geography twice as many students study history as geography.
Complete the Venn diagram.
One student in Year 10 is chosen at random from each school.
Work out the probability that they both study geography.
Was this exam question helpful?
Pupils from one primary school and one secondary school in Rochdale were asked,
“What is the main type of transport you use to travel to school?”
The table shows the results.
Main type of transport | Primary school | Secondary school |
Walk | 191 | 328 |
Bicycle 4 | 4 | 85 |
Car | 180 | 330 |
Bus 9 | 9 | 211 |
Other 6 | 6 | 36 |
Total | 390 | 990 |
One secondary school pupil is chosen at random.
Write down the probability that the pupil travels to school by bicycle.
One pupil is chosen at random from each school.
Work out the probability that both pupils travel to school by car.
In Rochdale,
22650 pupils attend primary school
13721 pupils attend secondary school.
Using the information in the table, estimate how many pupils in Rochdale travel to school by bicycle.
Give one reason why your answer to Question 4(c) might not be a good estimate.
Was this exam question helpful?
At a school, 32 students in Year 13 passed both parts of their driving test.
16 passed both the theory test and the practical test at the first attempt.
19 passed the theory test at the first attempt.
21 passed the practical test at the first attempt.
In the Venn diagram,
ξ represents the 32 students who passed their driving test
T represents the students who passed the theory test at the first
attempt
P represents the students who passed the practical test at the first
attempt
Complete the Venn diagram.
One student who passed their theory test at the first attempt is chosen at random.
Work out the probability that they also passed their practical test at the first attempt.
Two students are chosen at random.
Work out the probability that both students passed their theory test at the first attempt
Was this exam question helpful?
Matilda is going to compete in a cross-country running race.
The runners who finish first, second or third in the race will win a cash prize.
The table shows the value of the prize for each place.
Place | First | Second | Third |
Prize | £50 | £20 | £10 |
Matilda asked her coach to estimate the probability of her finishing in each of the first three places.
His estimates are in the table.
Place | First | Second | Third |
Probability | 0.15 | 0.55 | 0.2 |
Work out the coach’s estimate of the probability that Matilda will not win a prize.
Use the coach’s estimates to work out the expected value of Matilda’s prize.
Was this exam question helpful?
Between January and March 2020, 97.4% of trains were early or on time in the UK.
The rest of the trains were late.
Trains were late for one of three reasons.
The table shows the reasons why trains were late.
Reason | Percentage of late trains |
Extreme weather | 2.0% |
Rail infrastructure | 57.6% |
Train operation | 40.4% |
Work out the percentage of all trains that were late due to extreme weather.
Was this exam question helpful?
The owners of a business are concerned about the cost of employee absence.
Experience shows that 60% of employees are absent for at least one day per year.
Of those employees who are absent, 30% are absent for at least six days.
Complete the tree diagram.
Each employee costs the business £200 per day that they are absent.
The table shows the average number of days that employees are absent.
Absence in the year | Average number of days absent |
Fewer than six days | 3 |
At least six days | 12 |
Work out the expected cost of absence per employee per year.
The business can buy an Employee Absence insurance policy.
The policy costs £600 per employee per year.
The policy pays the business £150 per employee for each day they are absent.
Advise the business owners on whether they should buy the policy.
You should base your advice on the expected costs.
Was this exam question helpful?
There are 55 countries in the African Union.
In the Venn diagram,
ξ represents the 55 countries in the African Union
R represents the 45 countries with red in their flag
G represents the countries with green in their flag
Y represents the countries with yellow in their flag.
Complete the Venn diagram with the missing two numbers.
One of the countries is chosen at random.
Work out P(G ∪ Y)
Describe the flag of a country in the section R′ ∩ G
You do not need to work out the probability of choosing the country.
One of the countries with red in their flag is chosen at random.
Work out the probability that the flag also has yellow.
Was this exam question helpful?
A polygraph machine shows whether the answer to a question is the truth or a lie.
When a person answers a question, the polygraph shows one of two results.
Result | Meaning |
|---|---|
Truth | The polygraph believes the answer is the truth |
Lie | The polygraph believes the answer is a lie |
However, the result shown on the polygraph is not always correct.
When the answer is the truth, the polygraph incorrectly shows ‘Lie’ 10% of the time.
When the answer is a lie, the polygraph incorrectly shows ‘Truth’ 5% of the time.
A group of people are asked to test a polygraph by answering the question, “In what year were you born?”
80% of the group are told to answer with the truth.
The rest of the group are told to answer with a lie.
A person in the group is chosen at random to answer the question.
Work out the probability that the polygraph incorrectly shows ‘Lie’.
Each person in the group answers the question once.
The polygraph incorrectly shows ‘Lie’ 56 times to answers that are the truth.
The polygraph correctly shows ‘Lie’ x times to answers that are a lie.
Work out the value of 
.
One person in the group is chosen at random.
When this person answered the question the polygraph showed ‘Truth’.
Work out the probability that this person did tell the truth.
Was this exam question helpful?
A survey asked adults whether they suffered from asthma and whether they suffered from migraine.
The table shows the results.
Asthma | |||
Yes | No | ||
Migraine | Yes | 13 | 52 |
No | 28 | 398 | |
Work out the probability that an adult in the survey who suffers from asthma does not suffer from migraine.
In the UK, 5.4 million people suffer from asthma.
Use the information in the table to estimate the number of people in the UK who suffer from migraine.
Give one reason why your answer to question 3(b) might not be a good estimate
Was this exam question helpful?
A toy company has a contract to supply a new kind of toy for a supermarket.
The toy company will design and make the toys.
The packaging will be made by another company, based overseas.
When completed, the packaging will be delivered to the toy company by ship.
The toy company will then pack the finished toys and deliver them to the supermarket.
The table below lists the activities needed to deliver the toy to the supermarket.
The duration of each activity and its immediate predecessors are shown.
Task | Activity | Immediate predecessor(s) | Duration (days) |
A | Design toy | – | 8 |
B | Test toy | A | 7 |
C | Finalise toy design | B | 5 |
D | Make toy | C | 18 |
E | Write instructions for use | C | 2 |
F | Print instructions | E | 2 |
G | Design packaging | A | 2 |
H | Make packaging | G | 4 |
I | Deliver packaging | H | 23 |
J | Package toy | D, F, I | 3 |
K | Deliver toy to supermarket | J | 2 |
Draw a Gantt chart (cascade diagram) for the project.
The toy company has been warned that bad weather may cause the delivery of the packaging to take longer than the expected 23 days.
(i) What is the float, in days, for activity I (Deliver packaging)?
[1]
(ii) The company delivering the packaging estimates the probability of delay as follows.
Delay (days) | Probability |
0 | 0.08 |
1 | 0.21 |
2 | 0.35 |
3 | 0.30 |
4 or more | 0.06 |
Estimate the probability that the delivery of the toys to the supermarket will be delayed
[2]
1
14
15
23
Was this exam question helpful?
20 000 students enrolled at a university in 2017
Of these 20 000 students,
6800 students were aged 25 or over
10 800 students were female, and the rest were male
4400 were non-UK students, with 2000 of these being female.
Complete the Venn diagram.
Key: A aged 25 or over
B female
C non-UK
Use the Venn diagram to state how many male students from the UK aged under 25 enrolled at the university in 2017
A female student is chosen at random from the 20 000 students.
Work out the probability that she is aged under 25.
Give your answer as a fraction in its lowest terms.
Two students are chosen at random from the 20 000 students.
Work out the probability that one is a non-UK student and the other is from the UK.
Give your answer to two decimal places.
Was this exam question helpful?
A company has two offices, Office A and Office B, at different locations.
The company carries out a survey into the main ways of travelling to work by employees at both offices.
The results are shown in the table below.
Main way of travelling to work | Number of employees | |
Office A | Office B | |
Bus | 34 | 38 |
Train | 57 | 50 |
Car | 80 | 31 |
Bicycle | 22 | 36 |
Walking | 13 | 49 |
Other | 25 | 11 |
An employee is chosen at random from all employees who travel to work by bus or train.
Calculate the probability that the employee is from Office A.
One of the offices is in the centre of a town. The other office is in a business park, 10 miles outside the town.
State which office, A or B, is more likely to be in the centre of the town.
Give a reason for your answer.
Was this exam question helpful?
Hugo asks 40 students at his school if they have at home:
a smart TV
a dishwasher.
He uses their answers to construct the tree diagram below.
Hugo claims that, for these students, “having a smart TV” and “having a dishwasher” are independent.
Explain why Hugo’s claim is correct.
In Hugo’s school there are 1220 students.
(i) Estimate the number of students in Hugo’s school who have neither a smart TV nor a dishwasher at home.
[2]
(ii) State one assumption you made in the above question
[1]
Was this exam question helpful?
Statisticians collect data on the number of points won by tennis players when they are serving.
If the player gets their first serve in, they have a chance to win the point on their first serve.
If the player does not get their first serve in, they get a second serve and have a chance to win the point on that serve.
A statistician uses data about the tennis player Venus Williams to work out the probabilities in the table.
Event | Probability |
Venus gets her first serve in | 0.68 |
Venus wins the point if she gets her first serve in | 0.80 |
Venus wins the point if she does not get her first serve in | 0.49 |
Work out the probability of Venus Williams winning the point when she is serving.
For a particular tournament, a tennis racket manufacturer offers Venus Williams a bonus payment of 50 
dollars, where 
is the percentage of points that she wins when she is serving.
Estimate the expected bonus payment that Venus Williams receives.
The statistician works out the following probabilities for another tennis player, Johanna Konta, when she is serving.
Event | Probability |
Johanna gets her first serve in | 0.66 |
Johanna wins the point if she gets her first serve in | 0.75 |
Johanna wins the point if she does not get her first serve in |
|
The probability of Johanna Konta winning the point when she is serving is 0.69
Calculate the value of , giving your answer to two significant figures.
Was this exam question helpful?