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Data Handling and Probability - Probability scale from 0 (impossible) to 1 (certain)

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Probability is the mathematical word for the likelihood or chance of an event happening.

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The probability scale ranges from 0 to 1. It cannot be less than 0 or greater than 1.

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Probability of 0 means an event is 'Impossible' (e.g., rolling a 7 on a standard six-sided die).

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Probability of 1 means an event is 'Certain' (e.g., the sun rising tomorrow).

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Probability of 0.5 (or 1/2) means there is an 'Even Chance' (e.g., a coin landing on Heads).

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Values between 0 and 0.5 are described as 'Unlikely', while values between 0.5 and 1 are 'Likely'.

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Probability can be expressed as a fraction, a decimal, or a percentage.

📐Formulae

P(event)=Number of successful outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}}

P(event happening)+P(event NOT happening)=1P(\text{event happening}) + P(\text{event NOT happening}) = 1

💡Examples

Problem 1:

A bag contains 3 red marbles and 7 blue marbles. If you pick one marble without looking, what is the probability of picking a red marble? Express your answer as a fraction and describe it using a word from the probability scale.

Solution:

Fraction: 310\frac{3}{10}, Word: Unlikely

Explanation:

There are 3 successful outcomes (red marbles) out of a total of 10 marbles (3+7=103 + 7 = 10). Therefore, the probability is 3/103/10. Since 3/103/10 (0.3) is less than 1/21/2 (0.5), the event is described as 'Unlikely'.

Problem 2:

What is the probability of rolling a number less than 7 on a standard six-sided die (numbered 1 to 6)?

Solution:

1 (Certain)

Explanation:

All possible outcomes on a standard die (1, 2, 3, 4, 5, and 6) are less than 7. Since every possible outcome satisfies the condition, the probability is 6/66/6, which equals 1. This means the event is Certain.

Problem 3:

A spinner is divided into 4 equal sections: Green, Yellow, Blue, and Red. What is the probability of the spinner landing on 'Yellow'?

Solution:

14\frac{1}{4} or 0.25

Explanation:

There is 1 section for Yellow out of 4 equal total sections. The probability is 1á4=1/41 \div 4 = 1/4. On the probability scale, this is positioned halfway between 'Impossible' (0) and 'Even Chance' (0.5), making it 'Unlikely'.