3.1. Events, Sample Spaces, and Probability http://www.ck12.org
3.1 Events, Sample Spaces, and Probability
Learning Objectives
- Know basic statistical terminology.
- List simple events and sample space.
- Know the basic rules of probability.
Aneventis something that occurs or happens. Flipping a coin is an event. Walking in the park and passing by a
bench is an event. Anything that could possibly happen is an event.
Every event has one or more possibleoutcomes. Tossing a coin is an event but getting a tail is the outcome of the
event. Walking in the park is an event and finding your friend sitting on a bench is an outcome of the event.
In statistics, the process of taking a measurement or making an observation is called anexperiment.For example,
tossing a coin and recording the up face in a table of data is an experiment because a measurement is taken.
Experiment
The process of taking a measurement or making an observation.
Keep in mind that the definition of an experiment in statistics is broader than the one used in science. A scien-
tific experiment involves scientific instrumentations such as thermometers, microscopes, telescopes and tubes. A
statistical experiment may involve all these items but it mainly involves recording data and measurements. For
example, we may conduct an experiment to learn which brand of coffee a customer may prefer among three brands,
recording a voter’s opinion on a particular political issue, or measuring the amount of carbon monoxide present in a
certain environment. Any kind of observation, measuring, and recording that you may conduct can be considered a
statistical experiment.
Suppose a coin is tossed once. There are two possible outcomes, either a head(H)or a tail(T). Notice that if
the experiment is conducted only once, you will observe only one of the two possible outcomes. These individual
outcomes for an experiment are each calledsimple events. Here is another example: a die has six possible outcomes:
1 , 2 , 3 , 4 , 5 , 6 .When we toss it once, only one of the six outcomes of this experiment will occur. The one that does
occur is called a simple event.
Simple Event
The simplest outcome of an experiment.
Example:
Suppose that two pennies are tossed simultaneously. We could have both pennies land heads up (which we write as
HH), or the first penny could land heads up and the second one tails up (which we write asHT), etc. We will see