the cafeteria staff made sandwiches. each san...
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?
Answer
# Explanation:
## Step1: Calculate total types of sandwiches
Using the counting - principle, the number of ways to make a sandwich is the product of the number of choices for each component. There are 2 choices for bread (rye or white), 2 choices for meat (ham or turkey), and 2 choices for cheese (with or without cheese). So the total number of types of sandwiches is $2\times2\times2=8$.
## Step2: Calculate number of sandwiches with cheese
If the sandwich has cheese, there are 2 choices for bread and 2 choices for meat. So the number of sandwiches with cheese is $2\times2 = 4$.
## Step3: Calculate the probability
The probability $P$ of an event is the number of favorable outcomes divided by the number of total outcomes. The number of favorable outcomes (sandwiches with cheese) is 4, and the number of total outcomes is 8. So $P=\frac{4}{8}=\frac{1}{2}$.
# Answer:
$\frac{1}{2}$