4-member curling team is randomly chosen from 6 grade 11 students and 8 grade 12 students. What is the probability that the team has at least 2 grade 11 students?

0.5944 = 59.44% probability that the team has at least 2 grade 11 students

Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

In which:

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.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

We have that:

6 + 8 = 14 students, which means that

6 grade 11 students means that

Teams of 4 members means that

What is the probability that the team has at least 2 grade 11 students?

This is:

In which

So

Then

0.5944 = 59.44% probability that the team has at least 2 grade 11 students