Question

Select the correct answer.

Answer 1

Answer:

A 11.1%

Step-by-step explanation:

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

Hypergeometric distribution:

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

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question, we have that:

13 + 7 = 20 teachers, which means that N = 20.

7 history teachers means that k = 7.

Two teachers for each student, which means that n = 2.

What is the approximate probability that a random student on the trip will be assigned to a group led by two history teachers?

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,20,2,7) = \frac{C_{7,2}*C_{13,0}}{C_{20,0}} = 0.1105$

So close to 11.1%, and the correct answer is given by option A.