# simple statistics (binomial) terminology

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's.

My impression is that a single roll is called a trial.

What is the full 3-roll action called? I thought it was called an experiment, but I've seen experiment used synonymous with trial.

Using the binomial distribution, we call getting a 1 here a "success" and getting anything else a "failure." This might confuse students who think it's a "failure" to get three 1's. Is there an alternative/better way to say this acquiring of a 1 vs. not a 1?

• "ending up with two 1's" Do you mean exactly two or at least two? Apr 12, 2021 at 0:45
• I mean exactly two 1's. Apr 12, 2021 at 8:22
• You should edit your post to reflect that. Apr 12, 2021 at 8:51

• You might point out that the $$3$$-trial experiment has $$8$$ possible outcomes and $$256$$ possible events, which are subsets of the sample space; whereas each trial has $$2$$ possible outcomes, which can be contextually characterised as a success and a failure.

To distinguish between trial outcomes and experiment outcomes (or to remind about their distinction), I sometimes call the former “sub-outcomes” and the latter “elementary events”. When introducing the terminology, I indicate that “sub-outcome” is a nonstandard word (actually, I coined it).

In contrast, it is not so useful to call the event $$\{n11,1n1,11n\}$$ or its outcomes “successes”; moreover, we might be interested in multiple events in the experiment, in which case the notion of a “successful” event (or elementary event) will have to keep varying according to the event being considered.
• @Nights 1. Yes. And given enough discussion time, I might also point out that while any two trials of this experiment are independent of each other, two events with reference to this experiment could be either dependent or independent. $\quad$2. The sample space has $2^3=8$ members/outcomes and thus $2^8=256$ subsets/events. Apr 12, 2021 at 8:39
• 1. In your binomial model, each trial has exactly two possible outcomes: ‘1’ (success) and ‘n’ (failure, whose likelihood here is five times that of success). The game can of course be reframed as a different probability experiment in which each trial has six equally-likely outcomes; in this model, the experiment indeed has $6^3=216$ outcomes. Apr 12, 2021 at 10:11