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3 We also run a daily risk of getting sick. That is why it is sensible to protect our bodies and be aware of the ways to avoid being exposed to disease germs. For instance, people who touch their faces or food without making sure that their hands are clean after touching things like door handles, etc. that sick people may have been in contact with, are at greater risk of getting ailments like colds and flu.
4 People who often breathe in the second-hand cigarette smoke of others, run a significant risk of getting lung cancer or other lung diseases, especially if they are also often exposed to other polluted air.
UNCERTAINTY
When a patient is tested for a disease, the tests may be unreliable. This means that if, for example, the test is negative then there might still be a chance that you have the disease, and if the test is positive, there might be a chance that they don’t have the disease.
This is the reason why, for many serious diseases, a test is repeated after a while to see whether the result stays the same.
GAMBLING ODDS
We have seen that if you throw a die you have 1 chance in 6 of choosing the correct number. If you throw two dice ( a black one and a red one) and guess a number between 2 and 12, how likely are you to be correct?
If you guessed 12, then there is only 1 chance in 36 (P = 0,028) to be right. But if you said 3, then you have 2 chances out of 36 (P = 0,56) of getting it right, namely a 1 on the black die and a 2 on the red die OR the other way round. If you wisely guess 7, then you have 6 chances out of 36 (P = 0,167).
In the Lotto, it has been calculated that you have 1 chance in nearly 14 million of getting all six numbers correct if you guess once. This is a very low chance! On the other hand, it can be fun thinking what you would do with your winnings, if you won.
Source:
Pythagoras , Number 52, August 2000
| Learning outcomes(LOs) |
| LO 1 |
| Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems |
| Assessment standards(ASs) |
| We know this when the learner: |
| 1.2 recognises, uses and represents rational numbers (including very small numbers written in scientific notation), moving flexibly between equivalent forms in appropriate contexts; |
| 1.3 solves problems in context including contexts that may be used to build awareness of other learning areas, as well as human rights, social, economic and environmental issues such as: |
| 1.3.1 financial (including profit and loss, budgets, accounts, loans, simple and compound interest, hire purchase, exchange rates, commission, rental and banking); |
| 1.3.2 measurements in Natural Sciences and Technology contexts; |
| 1.4 solves problems that involve ratio, rate and proportion (direct and indirect); |
| 1.7 recognises, describes and uses the properties of rational numbers. |
| LO 5 |
| Data HandlingThe learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions and to interpret and determine chance variation. |
| We know this when the learner: |
| 5.1 poses questions relating to human rights, social, economic, environmental and political issues in South Africa; |
| 5.2 selects, justifies and uses appropriate methods for collecting data (alone and/or as a member of a group or team) which include questionnaires and interviews, e x periments, and sources such as books, magazines and the Internet in order to answer questions and thereby draw conclusions and make predictions about the environment; |
| 5.3 organises numerical data in different ways in order to summarise by determining: |
| 5.3.1 measures of central tendency; |
| 5.3.2 measures of dispersion; |
| 5.4 draws a variety of graphs by hand/technology to display and interpret data including: |
| 5.4.1 bar graphs and double bar graphs; |
| 5.4.2 histograms with given and own intervals; |
| 5.4.3 pie charts; |
| 5.4.4 line and broken–line graphs; |
| 5.4.5 scatter plots; |
| 5.5 critically reads and interprets data with awareness of sources of error and manipulation to draw conclusions and make predictions about: |
| 5.5.1 social, environmental and political issues (e.g. crime, national expenditure, conservation, HIV/AIDS); |
| 5.5.2 characteristics of target groups (e.g. age, gender, race, socio–economic groups); |
| 5.5.3 attitudes or opinions of people on issues (e.g. smoking, tourism, sport); |
| 5.5.4 any other human rights and inclusivity issues; |
| 5.6 considers situations with equally probable outcomes, and: |
| 5.6.1 determines probabilities for compound events using two-way tables and tree diagrams; |
| 5.6.2 determines the probabilities for outcomes of events and predicts their relative frequency in simple experiments; |
| 5.6.3 discusses the differences between the probability of outcomes and their relative frequency. |
Discussion
Probabilities
Some comments only – the learners will (with guidance) have fun with the statements.
1.4 Relevant again later on.
1.5 A statement that is very hard to judge.
1.6 Encourage learners to figure out that this can’t possibly be true.
1.8 True – as most class sizes are larger that 24, this means that more than half of the classes must have at least one pair of learners with the same birthday – let learners do some research.
2.1 Only 1 in 6
2.2 They will have to find some smarties and experiment!
2.4 True (unless the die is biased – and this does happen)
There are more aspects of risk that can be discussed – feel free to explore the subject with the learners if there is time.
Test
There is no test for this unit.
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