Question

the cafeteria creates pre - made boxed lunches with equal numbers of the following items: a sandwich made with either white or wheat bread and either roast beef or bologna a snack that is either chips, popcorn, or pretzels a drink that is either bottled water or juice if gretchen randomly chooses one of the boxed lunches, what is the probability that she will get a roast beef sandwich on wheat bread and popcorn in her box? 3/4 1/6 1/24 1/12

Explanation:

Step1: Calculate total lunch combinations

Use the counting principle. For sandwiches, there are $2\times2 = 4$ options (2 bread - types and 2 meat - types). For snacks, there are 3 options, and for drinks, there are 2 options. So the total number of lunch combinations is $4\times3\times2=24$.

Step2: Determine favorable combinations

There is 1 way to get a roast - beef sandwich on wheat bread, 1 way to get popcorn as a snack, and 2 ways to get a drink (but we are only interested in the combination with the specific sandwich and snack). The number of favorable combinations is $1\times1\times2 = 2$ (but since we are only concerned with the sandwich - snack part for the probability calculation here, we consider the favorable combination of just the sandwich and snack which is 1).

Step3: Calculate probability

The probability $P$ of an event is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{1}{24}$.

Answer:

$\frac{1}{24}$