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Statistics and Probability - The probability scale and simple outcomes

Grade 6IGCSE

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

🔑Concepts

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Probability is the measure of the likelihood that an event will occur.

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The Probability Scale ranges from 0 to 1 (or 0% to 100%).

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Probability terminology: 0 = Impossible, 0.5 = Even Chance, 1 = Certain.

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Intermediate values: Between 0 and 0.5 is 'Unlikely'; between 0.5 and 1 is 'Likely'.

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Probabilities can be expressed as fractions, decimals, or percentages.

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The sum of the probabilities of all possible mutually exclusive outcomes is always 1.

📐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(not Event)=1−P(Event)P(\text{not Event}) = 1 - P(\text{Event})

Sum of all Probabilities=1\text{Sum of all Probabilities} = 1

💡Examples

Problem 1:

A standard fair six-sided die is rolled. What is the probability of rolling an even number?

Solution:

P(even)=36=12P(\text{even}) = \frac{3}{6} = \frac{1}{2} or 0.50.5

Explanation:

A die has 6 possible outcomes {1, 2, 3, 4, 5, 6}. The even numbers are {2, 4, 6}, which are 3 successful outcomes. We divide 3 by the total 6.

Problem 2:

A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If one marble is picked at random, what is the probability it is NOT blue?

Solution:

P(not blue)=510=12P(\text{not blue}) = \frac{5}{10} = \frac{1}{2} or 0.50.5

Explanation:

Total marbles = 3 + 5 + 2 = 10. The number of 'not blue' marbles is Red + Green = 3 + 2 = 5. Alternatively, 1−P(blue)=1−510=5101 - P(\text{blue}) = 1 - \frac{5}{10} = \frac{5}{10}.

Problem 3:

On the probability scale, where would you place the event 'The sun will rise tomorrow'?

Solution:

At 1 (Certain).

Explanation:

Because it is a guaranteed event based on physical laws, its probability is 1, which represents 'Certain' on the scale.

Problem 4:

If the probability of it raining tomorrow is 0.3, what is the probability that it will stay dry?

Solution:

1−0.3=0.71 - 0.3 = 0.7

Explanation:

Since raining and staying dry are complementary events (they cover all possibilities), their sum must be 1. Therefore, P(dry)=1−P(rain)P(\text{dry}) = 1 - P(\text{rain}).