true or false, In a binomial experiment, the outcomes of each trial may be dependent on each other.
False. In a binomial experiment, the outcomes of each trial are assumed to be independent of each other.
False. In a binomial experiment, the outcomes of each trial are assumed to be independent of each other.
The statement "In a binomial experiment, the outcomes of each trial may be dependent on each other" is FALSE.
To understand why, let's first define a binomial experiment. A binomial experiment is a statistical experiment that satisfies the following four conditions:
1. There are a fixed number of trials, denoted as 'n'.
2. Each trial of the experiment can result in one of two possible outcomes, usually referred to as "success" or "failure."
3. The probability of success remains constant for each trial.
4. The trials are independent of each other, meaning the outcome of one trial does not affect the outcome of any other trials.
It's important to note that the key characteristic of a binomial experiment is the independence of the trials. This means that the outcomes of each trial are not dependent on each other.
For example, let's consider a binomial experiment where we flip a fair coin 3 times. In this experiment, the outcome of each trial (head or tail) is independent of the previous or future trials. The result of the first flip does not affect the result of the second or third flip.
Therefore, in a binomial experiment, the outcomes of each trial are by definition assumed to be independent and not dependent on each other. So, the statement is false.