Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Probability is the mathematical word for the likelihood or chance of an event happening.
The probability scale ranges from 0 to 1. It cannot be less than 0 or greater than 1.
Probability of 0 means an event is 'Impossible' (e.g., rolling a 7 on a standard six-sided die).
Probability of 1 means an event is 'Certain' (e.g., the sun rising tomorrow).
Probability of 0.5 (or 1/2) means there is an 'Even Chance' (e.g., a coin landing on Heads).
Values between 0 and 0.5 are described as 'Unlikely', while values between 0.5 and 1 are 'Likely'.
Probability can be expressed as a fraction, a decimal, or a percentage.
📐Formulae
💡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: , Word: Unlikely
Explanation:
There are 3 successful outcomes (red marbles) out of a total of 10 marbles (). Therefore, the probability is . Since (0.3) is less than (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 , 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:
or 0.25
Explanation:
There is 1 section for Yellow out of 4 equal total sections. The probability is . On the probability scale, this is positioned halfway between 'Impossible' (0) and 'Even Chance' (0.5), making it 'Unlikely'.