Binomial experiments are those where there is a fixed number of independent trials and only two outcomes. The outcome could be a yes/no answer. You might ask the question, “Will you get a head?” if you toss a coin. The answer will be either yes or no. This is the basic idea. However, in order to label an experiment a binomial one, you must also follow the following rules.
Understanding Binomial Distribution
The binomial in binomial distribution refers to two terms: the number of successful attempts and the number of failed attempts. Without the other, each is ineffective.
The binomial distribution is a common discrete distribution that is used in statistics. It is not a continuous distribution like normal. Binomial distribution counts only two states. This is due to the fact that it takes into account the number of trials. The binomial distribution is the probability of x success in n trials given a success probability (p) for each trial.
The Binomial distribution summarises the number of trials or observations when each trial has the exact same probability of reaching a particular value. The binomial distribution is a way to determine the likelihood of seeing a certain number of successful outcomes over a given number of trials.
- A fixed number of trials is required. This is obvious. If you do not have a fixed number of trials, you could continue to toss the coin for hours without stopping. You will also see a vastly different outcome if you throw the coin twice. For example, you could get two heads at once and conclude that you always get a head when you toss a coin! You could also toss it 100 times.
- Every trial is independent. Independent means that each time you do the trial again (i.e. Tossing the coin is an independent task. Each time you repeat the trial (i.e. If you toss ten coins at once and then remove the ones that have landed head down, it will affect the probability of the next coin being thrown. This is fine, but it wouldn’t be a binomial test. The fact that each trial can be performed independently of the others is a key aspect of binomial experiments. This means that the probability of success remains constant from one trial to the next.
- There are only 2 outcomes. Is it possible to find parking spaces in the city? Can eggs be boiled in less than ten minutes?
Binomial Experiment: Examples
- To see how many heads land on heads, toss a coin 100 times.
- Ask 100 people if you have been to Paris.
- To see if you roll a double, you need to roll two dice.
Experiments that aren’t Binomial Experiments
- Ask 100 people what their weight is. You’ll get 100 answers.
- Toss a coin until you have a head. It could take one, three, or six tosses, so there is no set number of trials. This is called a negative binary experiment.