Expressions of Probability Revision Notes for Grade 11 NSC Matric Mathematical Literacy

Expressions of Probability

What is probability?

Probability is a numerical value that tells us how likely an event is to happen. It's important to understand that probability gives us a prediction of what might occur, but it doesn't guarantee what will actually happen.

For example, when a weather forecast says there's a 30% chance of rain, this doesn't mean it will definitely rain. It simply means there's a possibility of rain, and we can use this information to help us make decisions (like whether to carry an umbrella).

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Think of probability as a way to measure uncertainty. It helps us make informed decisions even when we can't be completely certain about outcomes.

The basic probability formula

The fundamental way to calculate probability uses this formula:

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$P(\text{event}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

This formula always produces a fraction that compares how many ways something can happen to all the ways things could happen.

Three formats for expressing probability

Once you've calculated a probability using the basic formula, you can express your answer in three different ways:

1. Fraction format

The fraction format is the original form that comes directly from the probability formula
It shows the number of favourable outcomes compared to the total possible outcomes
Example: If you roll a die and want to get a 6, the probability is $\frac{1}{6}$

2. Decimal format

To get the decimal format, divide the numerator by the denominator of the fraction
Probability decimals are always between 0 and 1
A decimal of 0 means the event is impossible
A decimal of 1 means the event is certain
Example: $\frac{1}{6} = 0.167$ (rounded to 3 decimal places)

3. Percentage format

To get the percentage format, multiply the fraction by 100
Alternatively, multiply the decimal by 100
Percentages make probability easier to understand in everyday situations
Example: $\frac{1}{6} \times 100 = 16.7\%$

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Percentages are often the most intuitive format for understanding probability in real-world contexts, which is why weather forecasts, medical statistics, and survey results typically use percentages.

Converting between formats

Here's how to move between the three formats:

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Format Conversion Quick Reference:

Fraction → Decimal: Divide the top number by the bottom number
Fraction → Percentage: Multiply the fraction by 100
Decimal → Percentage: Multiply the decimal by 100
Percentage → Decimal: Divide the percentage by 100

Real-world applications

Probability appears in many everyday contexts:

News reports: Medical test accuracy might be expressed as percentages (e.g., "95% accurate")
Product advertising: Beauty products might claim "8 out of 10 women noticed improvement" (which equals $\frac{8}{10}$ or 80%)
Statistical data: Government reports use actual numbers that you must first convert to probabilities before making predictions

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Exam tip: When you see actual data (like crash statistics), remember to calculate the probability first using the basic formula before answering questions about likelihood.

Worked examples

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Worked Example 1: Rolling a die

Question: What's the probability of rolling an even number on a standard die?

Solution:

Favourable outcomes: 2, 4, 6 (that's 3 outcomes)
Total possible outcomes: 1, 2, 3, 4, 5, 6 (that's 6 outcomes)
Fraction: $P(\text{even}) = \frac{3}{6} = \frac{1}{2}$
Decimal: $\frac{1}{2} = 0.5$
Percentage: $0.5 \times 100 = 50\%$

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Worked Example 2: Drawing from a bag

Question: A bag contains 5 red balls and 3 blue balls. What's the probability of drawing a red ball?

Solution:

Favourable outcomes: 5 red balls
Total possible outcomes: 5 + 3 = 8 balls
Fraction: $P(\text{red}) = \frac{5}{8}$
Decimal: $\frac{5}{8} = 0.625$
Percentage: $0.625 \times 100 = 62.5\%$

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Worked Example 3: Converting formats

Question: Convert $\frac{3}{4}$ to decimal and percentage format.

Solution:

Decimal: $3 \div 4 = 0.75$
Percentage: $\frac{3}{4} \times 100 = 75\%$ or $0.75 \times 100 = 75\%$

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Key Points to Remember:

Probability is always a prediction - it tells us what might happen, not what will definitely happen
Use the basic formula $P(\text{event}) = \frac{\text{favourable outcomes}}{\text{total outcomes}}$ to calculate probability
Three formats exist: fraction (original), decimal (divide), percentage (multiply by 100)
Probability values range from 0 to 1
(or 0% to 100%) - anything outside this range is incorrect
In exams, always check whether you're given actual data or probability values, as this affects your approach to the problem

Expressions of Probability (Grade 11 NSC Matric Mathematical Literacy): Revision Notes