BINOMIAL EXPERIMENT

Definition Of Binomial Experiment

A binomial experiment is an experiment with a fixed number of independent trials

In a binomial experiment each trial has exactly two outcomes

The probability of each outcome in a binomial experiment remains the same for each trial

Examples of Binomial Experiment

Flip a coin 30 times to see how many heads you get.
Here,
The number of trials is fixed, 30, and each trial is independent of the other
The outcome can only be a head or a tail in each trial
The probability of getting a head is the same as the probability of getting a tail. So, its a binomial experiment

Video Examples: Binomial Experiments

Solved Example on Binomial Experiment

Ques: Choose whether the following is a binomial experiment. "Sandra rolled a 6-sided number cube until a 3 appeared."

Choices:

A. Yes
B. No
Corrected Answer: B

Solution:

Step 1: Sandra rolled the number cube until she saw a 3. So the number of trials is not fixed. So, its not a binomial experiment.

Quick Summary

Fixed number of trials
Independent trials
Two possible outcomes (success or failure)
Constant probability of success for each trial

\[ P(X = k) = \binom{n}{k} * p^k * (1-p)^{(n-k)} \]

🍎 Teacher Insights

Emphasize the importance of independent trials and constant probability. Use real-world examples to illustrate the concept.

🎓 Prerequisites

Probability
Independent Events

Check Your Knowledge

Q1: Which of the following is NOT a characteristic of a binomial experiment?

A. Fixed number of trials B. Independent trials C. More than two possible outcomes D. Constant probability of success

Q2: Rolling a die until you get a 6 is a binomial experiment.

A. True B. False

Frequently Asked Questions

Q: What is a trial in a binomial experiment?
A: A trial is a single instance of the experiment, such as flipping a coin once.

Q: What are the two possible outcomes?
A: The two possible outcomes are typically labeled as 'success' and 'failure'.