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?

The required probability is,

Step-by-step explanation:

P(A sandwich is made of roast beef) =

P(A snack is made of popcorn) =

Since, the two events, i. e., 'A sandwich is made of roast beef' and 'A snack is made of popcorn' are independent, so,

P(Gretchen will get a roast beef sandwich and popcorn in her box)

=

=

The probability is 1/6

Step-by-step explanation:

Let's define the following events:

A: get a roast beef sandwich.

B: get popcorn.

Given there are 2 possible sandwiches (bologna or roast beef), P(A) = 1/2

Given there are 3 possible snacks (chips, popcorn, or pretzels), P(B) = 1/3

These events are independent, then:

P(A ∩ B) = P(A) * P(B) = 1/2 * 1/3 = 1/6

where  P(A ∩ B) means Gretchen gets both a roast beef sandwich and popcorn.