Likelihood and probability scales (AQA GCSE Statistics): Revision Notes
Likelihood and probability scales
Understanding probability basics
Probability deals with how likely different outcomes and events are to happen. To understand probability properly, you need to grasp some key terms that form the foundation of this mathematical concept.
An outcome represents the result you get from a single trial or experiment. For instance, when you roll a dice once, the outcome is whichever number appears on top. Each roll gives you exactly one outcome.
An event describes a particular result that might include one or several different outcomes. For example, if you want to roll "a number greater than 4" on a dice, this event includes two possible outcomes: rolling a 5 or rolling a 6.
A trial refers to the actual process of carrying out an experiment, such as the physical act of rolling the dice or flipping a coin.
These three fundamental terms - outcome, event, and trial - work together to describe any probability situation. Understanding the difference between them is essential for solving probability problems correctly.
Describing likelihood with words
When discussing how likely something is to happen, mathematicians use specific terms that create a scale from impossible events to those that are guaranteed to occur.
The main likelihood terms you need to know are:
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Impossible events can never happen under any circumstances. These have zero chance of occurring.
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Unlikely events have a small chance of happening, but it's still possible they could occur.
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Evens (or "even chance") means an event is just as likely to happen as not to happen. This represents a 50/50 situation.
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Likely events have a good chance of happening, though they're not guaranteed.
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Certain events must happen - there's no way they can be avoided.
You can also use additional terms like "very unlikely" for events that are almost impossible, and "very likely" for events that are nearly certain to occur. These give you even more precision when describing probability.
The numerical probability scale
While words help us describe likelihood, mathematics uses numbers to be more precise about probability. The probability scale runs from 0 to 1, where each number corresponds to a specific level of certainty.
Here's how the numerical scale works:
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0 represents impossible events - these can never happen, so they have zero probability.
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0.5 represents evens - this is exactly half-way between impossible and certain, meaning there's an equal chance the event will or won't happen.
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1 represents certain events - these must happen, so they have maximum probability.
Events with probabilities between 0 and 0.5 are considered unlikely - the closer to 0, the more unlikely they become.
Events with probabilities between 0.5 and 1 are considered likely - the closer to 1, the more likely they become.
This numerical approach allows mathematicians to be extremely precise about probability, rather than relying only on descriptive words. Remember that probability values can only exist between 0 and 1 - you cannot have negative probabilities or probabilities greater than 1.
Worked examples
Let's look at some real-world situations and determine their likelihood:
Worked Example 1: "It will snow in London in May"
This would be classified as unlikely. While not completely impossible, snow in London during May is very rare due to the warmer spring temperatures.
Worked Example 2: "The next person born in the UK will be a boy"
This represents evens (or close to it). Statistically, there's approximately a 50/50 chance of any baby being male or female.
Worked Example 3: "Rolling a 7 on an ordinary dice"
This is impossible. Standard dice only have numbers 1 through 6, so rolling a 7 cannot happen.
These examples show how you can apply probability terms to everyday situations by considering the realistic chances of each event occurring.
Key mathematical facts
Remember these essential points about probability scales:
- Probability values always fall between 0 and 1 (inclusive)
- You can never have a probability less than 0 or greater than 1
- The closer a probability is to 0, the less likely the event
- The closer a probability is to 1, the more likely the event
- 0.5 represents perfect uncertainty - equally likely to happen or not happen
Remember!
Key Points to Remember:
- Probability measures how likely events are to occur, using both words and numbers
- The likelihood scale goes: Impossible → Unlikely → Evens → Likely → Certain
- Numbers from 0 to 1 represent probability, where 0 = impossible, 0.5 = evens, and 1 = certain
- Events between 0 and 0.5 are unlikely; events between 0.5 and 1 are likely
- You can describe the same probability using either words or numbers, depending on what's most appropriate for the situation