Using the hypergeometric distribution, it is found that there is a 0.0452 = 4.52% probability that this group of four students includes at least two of the top three geography students in the class.
The students are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.
<h3>What is the hypergeometric distribution formula?</h3>The <em>formula </em>is:
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There are 28 students in class, hence
.
- Four people will be chosen at random, hence
.
- The top three is composed by 3 people, hence
.
The probability that this group of four students includes at least two of the top three geography students in the class is:
In which:
Then:
0.0452 = 4.52% probability that this group of four students includes at least two of the top three geography students in the class.
You can learn more about the hypergeometric distribution at brainly.com/question/4818951
