Experiment
Experiment
In the study of probability, the name given to any controlled, repeatable process. For example, the following are all experiments: tossing a coin, rolling a die, or selecting a ball from a bag.
Often experiments are composed of multiple actions. For instance, simultaneously flipping a coin and rolling a die is an experiment.
See also
Worked Example
Problem: A bag contains 3 red balls and 2 blue balls. You draw one ball at random. Identify the experiment, the sample space, and one possible event.
Step 1: Identify the experiment. The experiment is the controlled, repeatable process being performed.
Step 2: The experiment here is: drawing one ball at random from the bag. You could repeat this process many times under the same conditions (replacing the ball each time).
Step 3: List the sample space — the set of all possible outcomes of this experiment. Since there are 3 red and 2 blue balls, each individual ball is a distinct outcome.
S={R1,R2,R3,B1,B2}
Step 4: Define an event. An event is any subset of the sample space. For example, the event 'drawing a red ball' is:
E={R1,R2,R3}
Step 5: Find the probability of this event by dividing the number of favorable outcomes by the total number of outcomes.
P(E)=53
Answer: The experiment is drawing one ball from the bag. The sample space has 5 outcomes. The event 'drawing a red ball' has probability 3/5.
Another Example
Problem: You roll a standard six-sided die twice. Describe the experiment and determine how many outcomes are in the sample space.
Step 1: Identify the experiment. The experiment is rolling a die two times in sequence. This is a compound experiment because it involves multiple actions.
Step 2: Each individual roll has 6 possible outcomes: 1, 2, 3, 4, 5, or 6.
Step 3: Since the two rolls are independent, use the counting principle to find the total number of outcomes in the sample space.
∣S∣=6×6=36
Step 4: Some example outcomes are (1, 1), (1, 2), ..., (6, 6). Each ordered pair represents one outcome of the experiment.
Answer: The experiment is rolling a die twice. Its sample space contains 36 outcomes.
Frequently Asked Questions
What is the difference between an experiment and an event in probability?
An experiment is the entire process you carry out, such as rolling a die. An event is a specific result or set of results you are interested in, such as 'rolling an even number.' The experiment produces outcomes; an event is a collection of one or more of those outcomes.
Can an experiment have an infinite number of outcomes?
Yes. For example, if the experiment is 'spin a spinner and record the exact angle where it stops,' the outcome could be any real number between 0° and 360°, giving infinitely many possible outcomes. In introductory courses, however, most experiments have a finite sample space.
Experiment vs. Outcome
An experiment is the entire process (e.g., rolling a die), while an outcome is a single specific result of that process (e.g., rolling a 4). One experiment produces exactly one outcome each time it is performed, but the sample space lists all outcomes that could occur.
Why It Matters
The concept of an experiment is the starting point for all probability calculations. Before you can find the probability of any event, you must first define the experiment so that you know what outcomes are possible. Clearly identifying the experiment also prevents confusion in compound situations, such as drawing two cards or flipping multiple coins, where the number of outcomes grows quickly.
Common Mistakes
Mistake: Confusing an experiment with an event.
Correction: The experiment is the process itself (e.g., flipping a coin). An event is a particular result or set of results you care about (e.g., getting heads). Always define the experiment first, then describe events within it.
Mistake: Forgetting that a compound experiment multiplies the number of outcomes.
Correction: When an experiment involves multiple actions — like rolling two dice — the total number of outcomes is the product of the outcomes from each action, not the sum. Rolling two dice gives 6 × 6 = 36 outcomes, not 6 + 6 = 12.
Related Terms
- Probability — Measures the likelihood of an experiment's outcomes
- Outcome — A single result produced by an experiment
- Sample Space — The set of all possible outcomes of an experiment
- Event — A subset of outcomes from an experiment
- Expected Value — The long-run average result of an experiment
- Trial — A single performance of an experiment
- Counting Principle — Used to count outcomes in compound experiments