Students sheet - Screening
Read the questions below and then give your initial responses. Make some brief notes to explain your reason(s) for each decision.
1. DNA is collected from a crime scene. Due to the nature of the crime, the police are certain this is the criminal’s DNA. The police have no leads to start with but then the DNA is matched to someone recorded on the National DNA database. The probability a random person’s DNA would match the sample is calculated to be 1 in 1000000.
How convinced would you be that the person is guilty?
Not at allA littleVery Certain
2. The government has a screening program for a potentially fatal medical condition which is thought to affect 1 in 1000 of the population. 100 000 people are tested.
The test is not completely accurate. It gives a positive result for 98 out of 100 patients with the condition. The test also gives a negative result for 98 out of 100 without the condition.
How worried should someone be if they have a positive result?
Not at allA littleVery Extremely
Read Q1 again and try to fill in the boxes indicated by the arrows below.
Now that you have these numbers to help you, how convinced are you that the person with matching DNA is guilty?
2. The government has a screening program for a potentially fatal medical condition which is thought to affect 1 in 1000 of the population. 100 000 people are tested.
The test is not completely accurate. It gives a positive result for 98 out of 100 patients with the condition. The test also gives a negative result for 98 out of 100 without the condition.
How worried should someone be if they have a positive result?
4. A company is considering introducing a filter to its email system to remove unwanted advertising mail which is sometimes referred to as SPAM. It is suggested that the filter will save time and prevent email storage capacity being wasted.
The SPAM filter has three different settings, light, normal and strict, which effects how many of the SPAM emails are filtered and how many genuine emails are incorrectly filtered out. The details are shown below.
Setting / Percentage of SPAM correctly filtered / Percentage of genuine emails incorrectly filteredLight / 90% / 2%
Normal / 95% / 3%
Strict / 99% / 5%
The company receives approximately 100 000 emails per week of which about 5% are SPAM.
Use the information above to find out how many of the company’s emails are likely to be affected by each of these settings.
State whether you would recommend the SPAM filter and give your reasons for this decision.
Students sheet - Making Estimates From Limited Information
At one time it was claimed that all of the world’s population could fit on the Isle of Wight. In 2011 the world’s population was estimated to be 7 billion; would this claim still be true?
Hint - The road distance from Freshwater to Newport shown in orange is approximately 20km.
Some further questions
How many pieces of luggage go through Heathrow airport in a year?
A company is considering opening a child day care centre in a town with a population of 200,000. There are 100 centres in the town at present. Use a quick estimate to evaluate the market for such a centre.
Five members of a swimming club plan to raise money for charity by attempting to swim around the coast of the Isle of Wight. Instead of one person swimming the whole distance they plan to take turns at swimming stages.
Is this activity feasible?
A food company is planning to bid for a franchise to supply pies to all of the football league grounds in the top four English divisions’ for a year. When interviewing someone to manage this project the panel asks them to estimate how many pies the company will need to produce during the year to fulfil the franchise. What would be a good answer to this question?
Students Sheets - VOTING SYSTEMS
School Trip
A group of 50 students are given 5 possible venues for a school reward trip. To make recording easy, each venue is assigned a letter A,B,C,D or E.
The students are asked to place the venues in order of preference starting with their favourite at the top.
When all of the lists are collected they are sorted into groups whose lists are identical. In total there are 6 groups. This information is given in the table below
For example group 1 is the preference list submitted by 18 of the students.
Choice / Group1 / Group 2 / Group 3 / Group 4 / Group 5 / Group 61st / A / B / C / D / E / E
2nd / D / E / B / C / B / C
3rd / E / D / E / E / D / D
4th / C / C / D / B / C / B
5th / B / A / A / A / A / A
Frequency / 18 / 12 / 8 / 7 / 3 / 2 / 50
The school plans to select just one venue.
Using the information in the table, suggest different ways to decide on a venue for the reward trip and choose the best way to decide where to go. You should explain how you arrived at your decision, and show your working to choose the venue for the trip.
Exploring the complications of different voting systems
Voting in the boardroom
Some companies operate a system where each share allows the owner one vote in ballots held to make key decisions. For example, if someone owns 100 shares their opinion is worth 100 votes whilst someone with 20 shares only gets 20 votes. Making a decision usually needs a simple majority of the votes.
In Company A there are two shareholders; Jamal has 60 shares, and Farouk has 40 shares.
In Company B there are three shareholders; Dinah has 48 shares, Gila has 46 shares, and Maya has 6 shares
In Company C there are four shareholders; Bala has 27 shares, Farah has 26 shares, Selma has 25 shares and Tripta has 22 shares.
Think carefully about how the decision making power is distributed in each of these companies. In each case give your opinions, with justification, on the fairness of the distribution of power.
Pets on the beach
The council of a holiday resort are trying to decide on whether they should allow pets on the beach. There are 5 members of the council each with equal voting rights. Three options are to be considered.
Option A – No pets allowed at any time on any area of the beach.
Option B – Pets would be allowed to use designated areas of the beach at any time.
Option C – Pets to be allowed on all areas of the beach at any time.
The decision will be made by using a preference list with a points system.3 points are awarded for a first choice, 2 for a second and 1 for a third choice. The option with the highest total will win the vote.
After talking to each of the members, Councillor Jones has discovered that the voting intentions are as shown in the table below.
CouncillorsArnold / Rashid / Masson / Jones / Ackroyd
First Choice / A / A / A / C / C
Second Choice / B / B / B / B / B
Third Choice / C / C / C / A / A
Which optionwould win the vote?
Councillors Jones and Ackroyd agree that A is their least preferred option. Suggest how theycould work together to obtain a more favourable option.
What measures could be put in place to avoid a repeat of this situation, and would you be in favour of this?