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? a. 2.3% b. 12.3% c. 11.1% d. 28.6%

Explanation:

Step1: Calculate total number of ways to choose 2 chaperones

The total number of teachers is \(7 + 13=20\). The number of ways to choose 2 chaperones out of 20 is given by the combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 20\) and \(r=2\). So \(C(20,2)=\frac{20!}{2!(20 - 2)!}=\frac{20\times19}{2\times1}=190\).

Step2: Calculate number of ways to choose 2 history - teachers

The number of history teachers is 7. The number of ways to choose 2 history - teachers out of 7 is \(C(7,2)=\frac{7!}{2!(7 - 2)!}=\frac{7\times6}{2\times1}=21\).

Step3: Calculate the probability

The probability \(P\) that a random student is assigned to a group led by two history teachers is the ratio of the number of ways to choose 2 history - teachers to the number of ways to choose 2 chaperones. So \(P=\frac{C(7,2)}{C(20,2)}=\frac{21}{190}\approx 0.111 = 11.1\%\).

Answer:

C. 11.1%