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 and popcorn in her box? 1/2 1/12 1/3 1/6

Explanation:

Step1: Calculate number of sandwich options

There are 2 types of bread and 2 types of meat for sandwiches. So number of sandwich options is $2\times2 = 4$.

Step2: Calculate number of snack options

There are 3 types of snacks, so number of snack options is 3.

Step3: Calculate number of drink options

There are 2 types of drinks, so number of drink options is 2.

Step4: Calculate total number of box - lunch combinations

By the multiplication principle, total number of box - lunch combinations is $4\times3\times2=24$.

Step5: Calculate number of favorable combinations

There is 1 way to get a roast - beef sandwich out of 4 sandwich options and 1 way to get popcorn out of 3 snack options, and 2 drink options. So number of favorable combinations is $1\times1\times2 = 2$.

Step6: Calculate the probability

Probability $P=\frac{\text{Number of favorable combinations}}{\text{Total number of combinations}}=\frac{2}{24}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$