Question

Select the correct answer.

The chaperones for a field trip to the museum will be 7 history teachers and 13 science teachers. Each student on the trip will be assigned to a
group led by two chaperones.
What is the approximate probability that a random student on the trip will be assigned to a group led by two history teachers?
O A
11.1%
ОВ.
2.3%
Ос.
28.6
OD. 12.3

Answer 1

Answer: 11.1%

Step-by-step explanation: Correct on Edmentum

Answer 2

A 11.1%

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) = (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) = (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) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

`P(X = 2) = h(2,20,2,7) = (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.