dentify the statements that explain why this is a binomial experiment. Select all that apply.
A.
The probability of success is different for each trial of the experiment.
B.
The trials are independent.
C.
The probability of success is the same for each trial of the experiment.
D.
Each trial depends on the previous trial.
E.
The experiment is performed a fixed number of times.
F.
There are two mutually exclusive​ outcomes, success​ (plane arrives on​ time) or failure​ (plane does not arrive on​ time).
G.
There are three mutually exclusive possible​ outcomes, arriving​ on-time, arriving​ early, and arriving late.
H.
The experiment is performed until a desired number of successes is reached.

To identify the characteristics that explain why this is a **binomial experiment**, let's review the key criteria of a binomial experiment:

1. There are a **fixed number of trials**.
2. Each trial has only **two possible outcomes**: success or failure.
3. The **probability of success** is the **same for each trial**.
4. The trials are **independent** of each other.

Based on these criteria, the correct statements are:

- **B.** The trials are independent.  
- **C.** The probability of success is the same for each trial of the experiment.  
- **E.** The experiment is performed a fixed number of times.  
- **F.** There are two mutually exclusive outcomes, success (plane arrives on time) or failure (plane does not arrive on time).

### Explanations for incorrect options:
- **A.** The probability of success is different for each trial – Incorrect because the probability of success should remain **constant**.
- **D.** Each trial depends on the previous trial – Incorrect because binomial trials must be **independent**.
- **G.** There are three mutually exclusive possible outcomes – Incorrect because binomial experiments only have **two outcomes** (success or failure).
- **H.** The experiment is performed until a desired number of successes is reached – This describes a **geometric** experiment, not a binomial one.

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Would you like further details on binomial experiments or related concepts?

### Related Questions:
1. What are examples of real-world binomial experiments?
2. How does the binomial probability formula work?
3. Can the probability of success change during a binomial experiment?
4. What is the difference between a binomial and a geometric experiment?
5. How do you calculate the expected value in a binomial distribution?

### Tip:
Always check for independence and fixed probability of success to identify binomial experiments!

Identify the statements that explain why this is a binomial experiment. Select all that apply.
A. The probability of success is different for each trial of the experiment.
B. The trials are independent.
C. The probability of success is the same for each trial of the experiment.
D. Each trial depends on the previous trial.
E. The experiment is performed a fixed number of times.
F. There are two mutually exclusive outcomes, success (plane arrives on time) or failure (plane does not arrive on time).
G. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late.
H. The experiment is performed until a desired number of successes is reached.

Learn how to identify a binomial experiment by understanding key principles such as independent trials, fixed number of trials, consistent probability of success, and two mutually exclusive outcomes. Ideal for students in Grades 9-12 studying probability and binomial distributions.

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