Examples of binomial experiments

Here we show some examples of binomial experiments. But before we do so, what is a binomial experiment?

When an experiment satisfies the following four conditions, the experiment is called a binomial experiment.

• There are n identical trials to be performed.

• Each trial has only two possible outcomes, success or failure.

• The trials are independent.

• The probability of success or of failure remain constant, or is the same, for each trial.

Now, we will show a couple of good examples of binomial experiments to illustrate the concept.

Example #1

Consider the experiment of tossing a coin 6 times. This experiment is a binomial experiment.

There are a total of 6 trials or tosses and all 6 tosses are identical. In other words, we always toss a coin (not a die!) and the tossing of this coin is performed under identical conditions.

Each trial or toss has only two possible outcomes : a head or a tail. Depending on which outcome you are interested in, either head or tail could be called a success.

The trials are independent. For example, the outcome of a toss does not influence the outcome of another toss.

The probability of obtaining a tail is 0.5 and this will remain constant or never be different than 0.5. By the same token, the probability of obtaining a head is 0.5 and this will remain constant.

Example #2

Consider the experiment of testing a new drug with a success rate of 60%. The drug will be tested on 50 new patients. This is also a binomial experiment.

There are a total of 50 trials or tests and all 50 tests are identical. In other words, we always test the same medication under identical conditions.

Each trial or test has only two possible outcomes : the drug worked or the drug did not work.

The trials are independent. For example, the outcome of a test does not influence the outcome of another test.

The probability that the drug will work is 0.60 and this will remain constant or never be different than 0.6. By the same token, the probability that the drug will not work is 0.4 and this will remain constant.