- Calculate the probability of an event in a chance experiment.
- Recognize the differences between theoretical and empirical probability.
What is Probability?
probability
Probability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity.
An experiment is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said to be a chance experiment. A chance experiment involves making observations in situations where there is uncertainty about which of two or more possible outcomes will result. Flipping one fair coin is an example of a chance experiment.
sample space
The sample space of a chance experiment is the collection of all possible outcomes for the experiment.
The uppercase letter [latex]S[/latex] is typically used to denote the sample space.
Let’s see if we can simulate chance experiments to understand probability.
Step 1: Select the Coin Flips tab.
Step 2: On How many flips do you want to generate in one simulation?, enter [latex]1[/latex], [latex]10[/latex], [latex]100[/latex], [latex]1000[/latex], and [latex]10,000[/latex], one after another.
Step 3: Select Generate.
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The proportions you found above from flipping a fair coin in [latex]1[/latex], [latex]10[/latex], [latex]100[/latex], [latex]1,000[/latex], and [latex]10,000[/latex] simulations were empirical probabilities.
empirical probabilities
The probability estimated from a chance experiment is called an empirical probability.