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. 11.1%
c. 12.3%
d. 28.6%

Explanation:

Step1: Calculate total chaperones

Total chaperones = $7 + 13 = 20$

Step2: Find total 2-chaperone groups

Use combination formula $C(n,k)=\frac{n!}{k!(n-k)!}$.
Total groups = $C(20,2)=\frac{20!}{2!(20-2)!}=\frac{20\times19}{2\times1}=190$

Step3: Find valid history teacher groups

Valid groups = $C(7,2)=\frac{7!}{2!(7-2)!}=\frac{7\times6}{2\times1}=21$

Step4: Compute probability

Probability = $\frac{\text{Valid groups}}{\text{Total groups}}=\frac{21}{190}\approx0.1105$

Step5: Convert to percentage

Percentage = $0.1105\times100\approx11.1\%$

Answer:

B. 11.1%