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Answer with explanation:
Binomial Experiment:
In a binomial experiment, if there are x Independent trials, there are only two possible outcome, one is Success and another one is failure.
The Probability of Success and failure in each trial is same.
Consider For example tossing a die,
Success(S)= Even Number={2,4,6}
Failure(F) =Odd Number ={1,3,5}
[tex]P(S)=\frac{3}{6}=\frac{1}{2}\\\\P(F)=\frac{3}{6}=\frac{1}{2}[/tex]
As, you throw the dice 100 times or 1000 times or 10000 times, the Probability of Success and failure in each case is same.And each throw will be independent of another.
The Three criteria that binomial experiments meet :
1.The trials are independent
2.There are only two outcomes per trial.
3. The probability of success is the same for each trial.
Three criteria do binomial experiments meet,
- b) The trials are independent.
- c) There are only two outcomes per trial.
- e) The probability of success is the same for each trial.
What is binomial experiments?
The binomial experiment is the experiment in which the total number of output values is 2, therefore it is known as binomial experiments. The number of independence variable in case of binomial experiments is fixed.
Both the two output has the 1/2 chances to occur.
Lets check all the given options which meet the binomial experiments criteria.
- a) There are only two trials- As the number of output value case of binomial experiment is two but the experiment has n number of identical trials. Thus this is incorrect criteria.
- b) The trials are independent- The number of independence variable in case of binomial experiments is fixed. Thus this criteria do binomial experiments meet.
- c) There are only two outcomes per trial- For the binomial experiment the total number of output values is 2. Thus, this criteria do binomial experiments meet.
- d) Each outcome is repeatable- For the binomial experiment each outcome may or may not be repeatable. Thus, this criteria do not binomial experiments meet.
- e) The probability of success is the same for each trial-Both the two output has the 1/2 chances to occur for the binomial experiment, half is for success and half is for failure. Thus, this criteria do binomial experiments meet.
Hence, three criteria do binomial experiments meet are,
- b) The trials are independent.
- c) There are only two outcomes per trial.
- e) The probability of success is the same for each trial.
Learn more about the binomial experiments here;
https://brainly.com/question/9325204
