Binomial experiment
A binomial experiment is an experiment where you have a fixed number of independent trials with only have two outcomes. For example, the outcome might involve a yes or no answer. If you toss a coin you might ask yourself “Will I get a heads?” and the answer is either yes or no. That’s the basic idea, but in order to call an experiment a binomial experiment you also have to make sure of the following four rules:- You must have a fixed number of trials. This should go without saying; if you don’t have a fixed number of trials you could be tossing that coin forever without stopping. In addition, the results from your experiment will be vastly different if you toss that coin twice (you could get two heads in a row and conclude that you will always get a heads if you toss a coin!) or if you toss it a hundred times .
- Each trial is independent of the others. “Independent” means that every time you repeat the trial (i.e. tossing that coin), it’s a fresh new trial and nothing you do has an effect on each coin toss. For example, if you tossed ten coins at a time and removed the coins that landed heads down before throwing again, you’ll affect the probability, because there are fewer coins. There’s nothing wrong with that, but it would not be a binomial experiment! The fact that each trial is independent of each other leads to another important aspect of binomial experiments; the probability remains constant from trial to trial.
- There are only two outcomes. In other words, if you can phrase the experiment as a yes or no answer, then it can be a binomial experiment: will I get a heads? Can someone find a parking space in the city? Do eggs hard boil in ten minutes?
Examples of a Binomial Experiment:
- Tossing a coin a hundred times to see how many land on heads.
- Asking 100 people if they have ever been to Paris.
- Rolling two dice to see if you get a double.
Examples of experiments that are not Binomial Experiments
- Tossing a coin until you get a heads (it could take one toss, or three, or six, so there is not a fixed number of trials)
- Asking 100 people how much they weigh (you’ll have a hundred possible answers, not two)…
