Mathematics
Grade 7
15 min
Calculate probability
Calculate probability
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1
Introduction & Learning Objectives
Learning Objectives
Define key probability terms such as outcome, event, and sample space.
Identify all possible outcomes for a simple event.
Calculate the theoretical probability of a simple event.
Calculate the experimental probability of an event based on observed data.
Express probability as a fraction, decimal, or percentage.
Compare and contrast theoretical and experimental probabilities.
Describe the likelihood of an event using terms like impossible, unlikely, equally likely, likely, and certain.
Have you ever wondered what your chances are of winning a game or if it will rain tomorrow? 🌧️ Probability helps us understand how likely something is to happen!
In this lesson, you'll learn how to calculate the probability of different events. We'll explore how...
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Key Concepts & Vocabulary
TermDefinitionExample
OutcomeA single possible result of an experiment or situation.When you flip a coin, 'heads' is an outcome, and 'tails' is another outcome.
EventOne or more outcomes of an experiment.When rolling a standard six-sided die, rolling an 'even number' is an event. The outcomes for this event are 2, 4, and 6.
Sample SpaceThe set of all possible outcomes for an experiment.For rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
Favorable OutcomeAn outcome that meets the specific condition of the event you are interested in.If the event is 'rolling a number greater than 4' on a die, the favorable outcomes are 5 and 6.
Theoretical ProbabilityThe probability of an event based on reasoning and what *should* happen, ass...
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Core Formulas
Theoretical Probability Formula
$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
Use this formula when you want to calculate the probability of an event based on what should happen, without actually performing an experiment. It assumes all outcomes in the sample space are equally likely.
Experimental Probability Formula
$P(\text{event}) = \frac{\text{Number of times the event occurred}}{\text{Total number of trials}}$
Use this formula when you have collected data from an experiment or observation. It tells you the probability of an event based on what actually happened during the trials.
Probability Range
$0 \le P(\text{event}) \le 1$
The probability of any event will always be a number between 0 and 1, inclusiv...
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Challenging
A basketball player has an experimental probability of making a free throw of 80%. Based on this data, how many free throws would you expect them to make in their next 50 attempts?
A.80
B.50
C.8
D.40
Challenging
A bag contains a total of 30 marbles which are red, green, or blue. The probability of picking a red marble is 1/3. The probability of picking a green marble is 2/5. How many blue marbles are in the bag?
A.10
B.8
C.12
D.22
Challenging
A spinner is divided into 4 equal sections: Red, Blue, Green, Yellow. After 120 spins, the results are: Red (32), Blue (28), Green (31), Yellow (29). Which statement best describes the relationship between the probabilities?
A.The experimental probabilities are close to the theoretical probability, which is expected with a large number of trials.
B.The experimental probability for Red is much higher than its theoretical probability, suggesting the spinner is unfair.
C.The theoretical probability of landing on any color is 0, because the spinner never lands perfectly on the line.
D.The experimental and theoretical probabilities are exactly the same.
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