2 the cafeteria staff made sandwiches. each sandwich had either rye or white bread, either ham or turkey…

2 the cafeteria staff made sandwiches. each sandwich had either rye or white bread, either ham or turkey, and either cheese or no cheese. the staff made an equal number of each type of sandwich. the sandwiches were placed on a tray. without looking, mary will choose a sandwich. what are the chances that mary will get a sandwich with cheese?\na $\frac{1}{8}$\nb $\frac{1}{6}$\nc $\frac{1}{3}$\nd $\frac{1}{2}$

2 the cafeteria staff made sandwiches. each sandwich had either rye or white bread, either ham or turkey, and either cheese or no cheese. the staff made an equal number of each type of sandwich. the sandwiches were placed on a tray. without looking, mary will choose a sandwich. what are the chances that mary will get a sandwich with cheese?\na $\frac{1}{8}$\nb $\frac{1}{6}$\nc $\frac{1}{3}$\nd $\frac{1}{2}$

Answer

Explanation:

Step1: Calculate total sandwich types

Use the counting principle. There are 2 types of bread, 2 types of meat, and 2 options for cheese. So the total number of sandwich - types is $2\times2\times2=8$.

Step2: Calculate number of sandwiches with cheese

For sandwiches with cheese, there are 2 types of bread, 2 types of meat, and 1 option (with cheese). So the number of sandwiches with cheese is $2\times2\times1 = 4$.

Step3: Calculate the probability

The probability $P$ of getting a sandwich with cheese is the number of favorable outcomes (sandwiches with cheese) divided by the number of total outcomes (all sandwiches). So $P=\frac{4}{8}=\frac{1}{2}$.

Answer:

D. $\frac{1}{2}$