Question

a cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. there are two students in line and each will take a sandwich. what is the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich? 1/7 1/14 2/15 2/21

Explanation:

Step1: Calculate total number of sandwiches

The total number of sandwiches is $5 + 6+4=15$.

Step2: Calculate probability of first - student taking cheese sandwich

The probability that the first student takes a cheese sandwich is $\frac{6}{15}$ since there are 6 cheese sandwiches out of 15 total sandwiches.

Step3: Calculate probability of second - student taking turkey sandwich

After the first student takes a sandwich, there are 14 sandwiches left. The probability that the second student takes a turkey sandwich is $\frac{5}{14}$ since there are 5 turkey sandwiches left out of 14 remaining sandwiches.

Step4: Calculate combined probability

Since these are independent - like sequential events, we multiply the probabilities. The combined probability is $\frac{6}{15}\times\frac{5}{14}=\frac{30}{210}=\frac{1}{7}$.

Answer:

A. 1/7