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

Explanation:

Step1: Calculate total number of teacher - combinations

The total number of teachers is \(7 + 13=20\). The number of ways to choose 2 teachers 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 combinations of 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 group is led by 2 history teachers is the number of favorable outcomes (groups led by 2 history teachers) divided by the number of total outcomes (all possible groups of 2 teachers). So \(P=\frac{C(7,2)}{C(20,2)}=\frac{21}{190}\approx 0.1105 = 11.05\%\approx11.1\%\).

Answer:

A. 11.1%