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Assessing risk in engineering, work and life
Assessing risk in engineering, work and life

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3.1 Expressing probability

Probability can be expressed mathematically in a number of ways. The following all show an equal probability:

  • as a proportion (e.g. 1 in 8)
  • as a decimal number between 0 and 1 (e.g. 0.125)
  • as a fraction (e.g. one divided by eight )
  • as a percentage (e.g. 12.5%).

An impossible event has a probability of 0, while an event that is certain to happen has a probability of 1. For instance, the probability of dying (eventually) is 1.0 (or 100%) for everyone.

Figure 12 illustrated scales of risk reduction. This is revisited in Table.3, where probabilities (or risks) are expressed in the different standard forms, including scientific notation as a useful reminder.

Table 4 Expressions of risk
ProportionDecimalFractionPercentageScientific notation
1 in 20.5one divided by two50%5 ×10−1
1 in 50.2one divided by five20%2 ×10−1
1 in 100.1one divided by 1010%1 ×10−1
1 in 1000.01one divided by 1001%1 ×10−2
1 in 10000.001one divided by 10000.1%1 ×10−3
1 in 10 0000.0001one divided by 10 postfix times 0000.01%1 ×10−4
1 in 100 0000.000 01one divided by 100 postfix times 0000.001%1 ×10−5
1 in 1 000 0000.000 001one divided by one postfix times 000 postfix times 0000.0001%1 ×10−6
1 in 10 000 0000.000 000 1one divided by 10 postfix times 000 postfix times 0000.000 01%1 ×10−7

Professional risk analysts often quote various figures showing the risks associated with everyday activities in comparison to risks in which they have an interest. Some examples from one published table of risks are included in Table 4. However, remember that all such tables and figures are based on historical information and cannot always be relied upon for future predictions.

Table 5 Levels of fatal risk in the UK (approximate averages), given as the chance of each event occurring per year
Risk of dying in a yearActivity
1 in 100Five hours of solo rock climbing every weekend
1 in 1000Working in a high-risk group within the more hazardous industries
1 in 10 000General travelling by road or on foot
1 in 100 000Working in the very safest parts of industry
1 in 1 000 000Fire caused by a cooking appliance at home
1 in 10 000 000Being hit by lightning
(Source: HSE, 1992)

One obvious reason why future risks cannot be predicted easily is that all professions are constantly working to improve safety. Therefore the two industrial death probabilities quoted above will now be lower. The number of car accidents, for example, has diminished rapidly in recent decades in the UK, and injury rates have also decreased with the mandatory use of safety belts and the installation of airbags, impact-protected body shells and better tyres. Improvements to road design and layouts have also played a part here. These improvements do not mean that we should be complacent; there are almost always additional ways in which death and injury rates can be reduced yet further.

Activity 3 Risk in scientific notation

Timing: Allow approximately 20 minutes.

Complete the following table to express the risks shown in terms of a decimal, a fraction and scientific notation.

Table 6 Risks shown in decimal, fraction and scientific notation
DecimalFractionScientific notation
1.6 ×10−2
one divided by 150
one divided by three postfix times 000 postfix times 000


Table 7 Answers for risks shown in decimal, fraction and scientific notation
DecimalFractionScientific notation
0.05one divided by 205 ×10−2
0.016one divided by 62.5 or two divided by 1251.6 ×10−2
0.006 67one divided by 1506.67 ×10−3
0.000 000 333one divided by three postfix times 000 postfix times 0003.33 ×10−7

The important thing is to understand that although there might be a ‘1 in 10 million’ risk of death by lightning, or a ‘1 in 100’ risk of death from five hours of solo rock climbing every weekend, these figures may not show an accurate measure of risk from that activity. There are many other factors that might change these estimates – for instance, an individual might be a very safety-conscious rock climber or might make a habit of standing under trees during lightning storms.