How to distinguish trial and experiment in probability? I have checked Ross's definition and wikipedia's intro on the definition of them for a while, but not quite get it till now. What is the difference of them? And when it comes to Bernoulli trail or Bernoulli experiment, do we call Bernoulli trial, or Bernoulli trials, or Bernoulli experiment, or Bernoulli experiments?
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The short answer is "context". A trial can be reframed/recontexualised into an experiment, and vice versa. For example, the 3-trial experiment Mary flipping three coins might be one trial of the 2-trial experiment Mary and John each flipping 3 coins. – ryang Aug 09 '22 at 09:53
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Strictly speaking, any particular performance of a random experiment is called a trial.
We know that a random experiment can be repeated under similar conditions. One such specific repetition of the experiment is what is meant by a trial. So if I consider a random experiment of tossing a fair coin twice, then one particular toss will be referred to as a trial.
StubbornAtom
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- If consider an experiment "toss a coin and then toss a dice", is each "sub-experiment", though being quite different kind, still called a trial? 2) Is there a standard name for something like "composed experiment" (or "successive experiment"?), refering to succesively performing some experiment, and such process forms an experiment? The text I only have is Ross', I remember he didn't give a name for this, weird.
– Eric Jun 04 '18 at 18:10 -
@Eric (1) Yes, an experiment can comprise different types of trials, so its sample space could be ${1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}.$ I wish the terminology had a specific word for a trial's outcome (say, $H$), because I often find myself informally saying "sub-outcome" to distinguish it from the experiment's outcome (say, $2H$). – ryang Dec 10 '20 at 17:31
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I am giving my description on the basis of the notes taken during my probability class.
Any particular performance of a random experiment is a trial.
By Experiment or Trial in the subject of probability, we mean a random experiment unless otherwise specified. Each trial results in one or more outcomes.
For example
$1)$ Tossing $4$ coins
$2)$ Picking $3$ balls from a bag containing $10$ balls $4$ of which are red and $6$ blue
$3)$ Rolling a die
Trial vs Experiment
Many times we use the words trials and experiment synonymously. Both trial and experiment mean something that is done in anticipation of a result. However, we sometimes use the two terms together attributing a slightly different sense to the two terms.
Where you are required to differentiate between a trial and an experiment, consider the experiment to be larger entity formed by the combination of a number of trials.
For example,
$1)$In the experiment of tossing $4$ coins, wew may consider tossing each coin as a trail and therefore say that there are $4$ trails in the experiment.
$2)$In the experiment of picking $3$ balls from a bag containing $10$ balls $4$ of which are red and $6$ blue, we can consider picking each ball to be an event and therefore say that there are $3$ trails in the experiment.
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I see. I find that there may be two opposite way to think about such question, which is better, or equally good? One is as you mentioned: given an experiement, we can divide it into many "trials" to analyze it, if necessary. The other, we treat every single step as an experiment, and think about the whole successive performance of them as a combined experiment. For the latter, do we use the term like "composite experiment" or "combined experiment" or "successive experiment" an experiment that is made by doing many subexperiments? ... – Eric Jun 11 '18 at 05:21
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...I saw Feller informally used it in his text, but he didn't explicitly give a defintion for such thing. – Eric Jun 11 '18 at 05:21
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To be clear, a question bumped into my mind. Adam, Brian, Cody three people both shoot an arrow to the same target. An arrow for each person. Suppose the rate they can successifully hit the target are $0.9$, $0.7$ and $0.5$ respect, and consider their shoot don't affect each other. What is the probability that these three person both successifully hit the target? For such question, should we consider the sample space as ${(H,H,H),~(H,H,L),~(H,L,H),~(H,L,L),~\cdots\cdots,~(L,L,L)}$ (ps: $H$ for hit, and $L$ for lost), and the event that Adam hit means ${(H,H,H),~(H,H,L),~(H,L,H),~(H,L,L)}$? – Eric Jun 11 '18 at 05:26
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@Eric Yes re: the suggested sample space and event re: Adam,Brian, Cody. – ryang Dec 10 '20 at 17:36
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Experiment is the some activity whose outcomes are sometimes known to us and sometimes not. For example, "After many experiments Edison was able to invent an electric bulb. This was an experiment in which were not having any idea about what will be the outcome. Experiment in which we know that our outcome will from some possible out comes that are known to us, for example, when we roll a dice, we know that, the outcome will be either from "1,2,3,4,5,6". There will be know outcome other than these six numbers. We call such experiments as random experiments.
Trial- When we repeat a experiment many times, then each of that performed experiment is known as trail.
Use following link for reference-
https://www.cuemath.com/data/terms-of-probability/
