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Binomial experiment: How to figure out what is and what isn’t

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Binomial experiment: Four Steps

binomial experiment

A coin toss can be a binomial experiment.


Determining if a question concerns a binomial experiment involves asking yourself four questions about the problem. It’s as simple as that!

Sample question: which of the following are binomial experiments?

  1. Telephone surveying a group of 200 people to ask if they voted for George Bush.
  2. Counting the average number of dogs seen at a veterinarian’s office daily.
  3. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time.
  4. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.”

Step 1:Ask yourself: is there a fixed number of trials?

  • For question #1, the answer is yes (200).
  • For question #2, the answer is no, so we’re going to discard #2 as a binomial experiment.
  • For question #3, the answer is yes, there’s a fixed number of trials (the 50 traffic lights).
  • For question #4, the answer is yes (your 6 darts).

Step 2: Ask yourself: Are there only 2 possible outcomes?

  • For question #1, the only two possible outcomes are that they did, or they didn’t vote for Mr. Bush, so the answer is yes.
  • For question #3, there are 3 possibilities: red, green, and yellow, so it’s not a binomial experiment.
  • For question #4, the only possible outcomes are WIN or LOSE, so the answer is yes.

Step 3:  Ask yourself: are the outcomes independent of each other? In other words, does the outcome of one trial (or one toss, or one question) affect another trial?

  • For question #1, the answer is yes: one person saying they did or didn’t vote for Mr. Bush isn’t going to affect the next person’s response.
  • For question #4, each time you toss a dart, the number of winning and losing tickets changes, which means, for example, if you win one toss, the probability of winning isn’t 10 to 10 anymore, but 9 to 10, since you already have one of the winning tickets. Since the probability is different, the trials are not independent, so the answer is no, and question #4 is not a binomial experiment.

Step 4: Does the probability of success remain the same for each trial?

  • For question #1, the answer is yes, each person has a 50% chance of having voted for Mr. Bush.

Question #1 out of the 4 given questions was the only one that was a binomial experiment.

For more on coin toss examples, see this article at the University of Western Michigan.

12 thoughts on “Binomial experiment: How to figure out what is and what isn’t

  1. Lisa Barcomb

    this information was very helpful in doing chapter 3, even thou it was a bit hard and I had to read it several times in order to get the jest of it and this article pretty much asked the questions that I was looking for. I thought it was good for the most part

  2. Rebecca Gamble

    This blog actually helped me understand some of the problems in chapter 3. At first I thought that question #2
    “Counting the average number of dogs seen at a veterinarian’s office daily”, was a binomial experiment because it could be in trials seeing that you would need the average. Then again the average would more then likely be not fixed. I think I going to go back in rework some of those practice questions now that I have this help.

  3. Mark McCrea

    I am having a time trying to understand this chapter. Question 2 is the question that has me at a stand still.

  4. Donna Allen

    This explanation was helpful. It’s much easier to understand something when it’s explained step by step with examples.

  5. Catherine Flanagan

    This blog was very helpful in understanding binomials. I like how the steps are broken down and three different examples are given so I could see what was a binomial and was not. I do have a question though, example 1 is also a binomial correct?

  6. angie widdows

    This was a very helpful example. I am not sure if I could take this class without your examples

  7. David

    In step 4 for Question #1 I’m not sure you can assume each individual response has a 50% probability of voting for Bush and that this is thus a binomial experiment. This would be saying then that the expected value of people voting for Bush out of 200 is 100. Rather, if we knew ahead of time that the probablity of an individual voting for Bush is p, then here we would have 200 Bernoulli trials where the probability for each trial of voting for Bush is p. I liked your example of the situation that was not independent.

  8. Stephanie

    You could be right. When I wrote the article it looked close enough :) Sometimes it can be a close call…which is why figuring out if something is a binomial experiment is tricky!

    I guess if we want to get deep, the probability would depend on if the person called was Republican, Democrat etc.

    How about we assume we’re calling undecided voters (truly undecided, as in — could sway one way or another?)