Sample Space
Define and list sample spaces in Grade 9 probability: the set of all possible outcomes of an experiment, used to calculate probabilities by counting favorable outcomes over total outcomes.
Key Concepts
Property A sample space is the set of all possible outcomes of an event.
Examples When tossing a fair coin, the sample space of possible outcomes is {heads, tails}. For a standard number cube labeled 1 6, the sample space for a single roll is {1, 2, 3, 4, 5, 6}. If a spinner has four equal sections (blue, yellow, green, red), the sample space is {blue, yellow, green, red}.
Explanation Imagine listing every single possible thing that could happen in an experiment—that’s your sample space! Before you even roll a die, you know the possibilities are 1, 2, 3, 4, 5, or 6. This complete list of potential outcomes is the sample space. It's like knowing all the menu options before you order your food.
Common Questions
What is a sample space in probability?
A sample space is the set of ALL possible outcomes of a probability experiment. For rolling a die, the sample space is {1, 2, 3, 4, 5, 6}. For flipping a coin, it is {Heads, Tails}.
How do you list the sample space for a compound event?
Use a systematic tree diagram or organized list. For flipping a coin and rolling a die: pair each coin outcome (H, T) with each die outcome (1-6), giving 12 outcomes: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.
How is the sample space used to calculate probability?
Probability of an event = (number of favorable outcomes) / (total outcomes in sample space). If the sample space has 12 equally likely outcomes and 2 are favorable, the probability is 2/12 = 1/6.