How to distinguish trial and experiment?
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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$\begingroup$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.
$\endgroup$ 2 $\begingroup$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 trail.
By Experiment or Trail in the subject of probability, we mean a random experiment unless otherwise specified. Each trail 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
Trail vs Experiment
Many times we use the words trails and experiment synonymously. Both trail 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 trail and an experiment, consider the experiment to be larger entity formed by the combination of a number of trails.
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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